Making the extension to test with

It is unknown at this point if Sylius will even accept this..

Action/Api/BaseApiAwareAction.php

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+<?php
+namespace Alexrowesoap\Payumsagepay\Action\Api;
+
+use Payum\Core\Action\ActionInterface;
+use Payum\Core\ApiAwareInterface;
+use Payum\Core\ApiAwareTrait;
+use Payum\Core\GatewayAwareInterface;
+use Payum\Core\GatewayAwareTrait;
+use Alexrowesoap\Payumsagepay\Api;
+
+abstract class BaseApiAwareAction implements ActionInterface, GatewayAwareInterface, ApiAwareInterface
+{
+    use GatewayAwareTrait;
+    use ApiAwareTrait;
+
+    public function __construct()
+    {
+        $this->apiClass = Api::class;
+    }
+}

Action/AuthorizeAction.php

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+<?php
+namespace Alexrowesoap\Payumsagepay\Action;
+
+use Payum\Core\Action\ActionInterface;
+use Payum\Core\Bridge\Spl\ArrayObject;
+use Payum\Core\GatewayAwareInterface;
+use Payum\Core\GatewayAwareTrait;
+use Payum\Core\Request\Authorize;
+use Payum\Core\Exception\RequestNotSupportedException;
+
+class AuthorizeAction implements ActionInterface, GatewayAwareInterface
+{
+    use GatewayAwareTrait;
+
+    /**
+     * {@inheritDoc}
+     *
+     * @param Authorize $request
+     */
+    public function execute($request)
+    {
+        RequestNotSupportedException::assertSupports($this, $request);
+
+        $model = ArrayObject::ensureArrayObject($request->getModel());
+
+        throw new \LogicException('Not implemented');
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    public function supports($request)
+    {
+        return
+            $request instanceof Authorize &&
+            $request->getModel() instanceof \ArrayAccess
+        ;
+    }
+}

Action/CancelAction.php

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+<?php
+namespace Soapmedia\Payumsagepay\Action;
+
+use Payum\Core\Action\ActionInterface;
+use Payum\Core\Bridge\Spl\ArrayObject;
+use Payum\Core\Exception\RequestNotSupportedException;
+use Payum\Core\GatewayAwareTrait;
+use Payum\Core\Request\Cancel;
+
+class CancelAction implements ActionInterface
+{
+    use GatewayAwareTrait;
+
+    /**
+     * {@inheritDoc}
+     *
+     * @param Cancel $request
+     */
+    public function execute($request)
+    {
+        RequestNotSupportedException::assertSupports($this, $request);
+
+        $model = ArrayObject::ensureArrayObject($request->getModel());
+
+        throw new \LogicException('Not implemented');
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    public function supports($request)
+    {
+        return
+            $request instanceof Cancel &&
+            $request->getModel() instanceof \ArrayAccess
+        ;
+    }
+}

Action/CaptureAction.php

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+<?php
+namespace Alexrowesoap\Payumsagepay\Action;
+
+use Payum\Core\Action\ActionInterface;
+use Payum\Core\Bridge\Spl\ArrayObject;
+use Payum\Core\Exception\LogicException;
+use Payum\Core\Exception\UnsupportedApiException;
+use Payum\Core\GatewayAwareTrait;
+use Payum\Core\Reply\HttpRedirect;
+use Payum\Core\Request\Capture;
+use Payum\Core\Exception\RequestNotSupportedException;
+use Alexrowesoap\Payumsagepay\Api;
+use Alexrowesoap\Payumsagepay\Api\State\StateInterface;
+
+class CaptureAction implements ActionInterface
+{
+    use GatewayAwareTrait;
+
+    /**
+     * @var Api
+     */
+    protected $api;
+
+    /**
+     * {@inheritDoc}
+     */
+    public function setApi($api)
+    {
+        if (false === $api instanceof Api) {
+            throw new UnsupportedApiException('Not supported.');
+        }
+
+        $this->api = $api;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * @param Capture $request
+     */
+    public function execute($request)
+    {
+        RequestNotSupportedException::assertSupports($this, $request);
+
+        $model = ArrayObject::ensureArrayObject($request->getModel());
+        $token = $request->getToken();
+
+        if (isset($model['Status'])) {
+            return;
+        }
+
+        $details = $this->api->prepareOffsiteDetails($model->toUnsafeArray()); // filter model details for request
+
+        $missing = $this->api->getMissingDetails($details); // sagepay's api is wayward we should check for presence of required minimum
+
+        if (count($missing) > 0) {
+            throw new LogicException(
+                sprintf(
+                    'Missing: %s details are mandatory for current payment request!',
+                    implode(", ", array_keys($missing))
+                )
+            );
+        }
+
+        $model['state'] = StateInterface::STATE_WAITING;
+
+        // we do not need any sync action
+        // but payum by default do not set any afterUrl to notify token
+        if ($token) {
+            $model['afterUrl'] = $token->getAfterUrl();
+        }
+
+        $response = $this->api->createOffsitePurchase($details);
+
+        $responseArr = json_decode( $response->getBody()->getContents() );
+        $model['state'] = $responseArr['Status'] ==
+        Api::STATUS_OK || $responseArr['Status'] == Api::STATUS_OK_REPEATED ?
+            StateInterface::STATE_REPLIED :
+            StateInterface::STATE_ERROR;
+
+        /*$model->replace(
+            array_merge(
+                (array) $model->toUnsafeArray(),
+                (array) $response->toArray()
+            )
+        );*/
+
+        if ($responseArr['Status'] == Api::STATUS_OK ||
+            $responseArr['Status'] == Api::STATUS_OK_REPEATED
+        ) {
+
+            throw new HttpRedirect(
+                $responseArr['NextURL'] . '=' . $responseArr['VPSTxId']
+            );
+        }
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    public function supports($request)
+    {
+        return
+            $request instanceof Capture &&
+            $request->getModel() instanceof \ArrayAccess
+        ;
+    }
+}

Action/ConvertPaymentAction.php

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+<?php
+namespace Alexrowesoap\Payumsagepay\Action;
+
+use Payum\Core\Action\ActionInterface;
+use Payum\Core\Bridge\Spl\ArrayObject;
+use Payum\Core\Exception\RequestNotSupportedException;
+use Payum\Core\GatewayAwareTrait;
+use Payum\Core\Model\PaymentInterface;
+use Payum\Core\Request\Convert;
+use Payum\Core\Request\GetCurrency;
+
+class ConvertPaymentAction implements ActionInterface
+{
+    use GatewayAwareTrait;
+
+    /**
+     * {@inheritDoc}
+     *
+     * @param Convert $request
+     */
+    public function execute($request)
+    {
+        RequestNotSupportedException::assertSupports($this, $request);
+
+        /** @var PaymentInterface $payment */
+        $payment = $request->getSource();
+
+        $this->gateway->execute($currency = new GetCurrency($payment->getCurrencyCode()));
+        $divisor = pow(10, $currency->exp);
+
+        $details = ArrayObject::ensureArrayObject($payment->getDetails());
+
+        $details['VendorTxCode'] = $payment->getNumber();
+        $details['Amount'] = $payment->getTotalAmount() / $divisor;
+        $details['Currency'] = $payment->getCurrencyCode();
+        $details['Description'] = $payment->getDescription();
+        $details['CustomerEMail'] = $payment->getClientEmail();
+
+        $request->setResult((array) $details);
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    public function supports($request)
+    {
+        return
+            $request instanceof Convert &&
+            $request->getSource() instanceof PaymentInterface &&
+            $request->getTo() == 'array'
+        ;
+    }
+}

Action/NotifyAction.php

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+<?php
+namespace Alexrowesoap\Payumsagepay\Action;
+
+use Payum\Core\Action\ActionInterface;
+use Payum\Core\Bridge\Spl\ArrayObject;
+use Payum\Core\Exception\RequestNotSupportedException;
+use Payum\Core\Exception\UnsupportedApiException;
+use Payum\Core\GatewayAwareTrait;
+use Payum\Core\Request\GetHttpRequest;
+use Payum\Core\Request\Notify;
+use Alexrowesoap\Payumsagepay\Api;
+use Alexrowesoap\Payumsagepay\Api\Reply\NotifyResponse;
+use Alexrowesoap\Payumsagepay\Api\State\StateInterface;
+
+class NotifyAction implements ActionInterface
+{
+    use GatewayAwareTrait;
+
+    /**
+     * @var Api
+     */
+    protected $api;
+
+    /**
+     * {@inheritDoc}
+     */
+    public function setApi($api)
+    {
+        if (false === $api instanceof Api) {
+            throw new UnsupportedApiException('Not supported.');
+        }
+
+        $this->api = $api;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * @param Notify $request
+     */
+    public function execute($request)
+    {
+        RequestNotSupportedException::assertSupports($this, $request);
+
+        $model = ArrayObject::ensureArrayObject($request->getModel());
+
+        if (!isset($model['state']) ||
+            !in_array(
+                $model['state'],
+                array(
+                    StateInterface::STATE_REPLIED,
+                    StateInterface::STATE_NOTIFIED,
+                    StateInterface::STATE_CONFIRMED,
+                )
+            )
+        ) {
+            throw new RequestNotSupportedException("process only replied and notified payments");
+        }
+
+        $httpRequest = new GetHttpRequest;
+        $this->gateway->execute($httpRequest);
+
+        if ($httpRequest->method != 'POST') {
+            return;
+        }
+
+        $status = Api::STATUS_OK;
+        $model['state'] = StateInterface::STATE_NOTIFIED;
+        $notification = $httpRequest->request;
+        $redirectUrl = $model['afterUrl'];
+        // check signature hash
+
+        if ($this->api->tamperingDetected((array) $notification, (array) $model->toUnsafeArray())) {
+            $status = Api::STATUS_INVALID;
+            $statusDetails = "Tampering detected. Wrong hash.";
+        } else {
+            if ($notification['Status'] == Api::STATUS_OK) {
+                $model['state'] = StateInterface::STATE_CONFIRMED;
+            } elseif ($notification['Status'] == Api::STATUS_PENDING) {
+                $model['state'] = StateInterface::STATE_REPLIED;
+            } else {
+                $model['state'] = StateInterface::STATE_ERROR;
+            }
+
+            $statusDetails = 'Transaction processed';
+
+            if ($notification['Status'] == Api::STATUS_ERROR
+                && isset($notification['Vendor'])
+                && isset($notification['VendorTxCode'])
+                && isset($notification['StatusDetail'])
+            ) {
+                $status = Api::STATUS_ERROR;
+                $statusDetails = 'Status of ERROR is seen, together with your Vendor, VendorTxCode and the StatusDetail.';
+            }
+
+        }
+
+        $model['notification'] = (array) $notification;
+        $model->replace(
+            $model->toUnsafeArray()
+        );
+
+        $params = array(
+            'Status' => $status,
+            'StatusDetails' => $statusDetails,
+            'RedirectURL' => $redirectUrl,
+        );
+
+        throw new NotifyResponse($params);
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    public function supports($request)
+    {
+        return
+            $request instanceof Notify &&
+            $request->getModel() instanceof \ArrayAccess
+        ;
+    }
+}