Hi,
Yes. This comes from the code of the QuickPay plugin :
$order_status = $this->payment_params->invalid_status;
$history->data .= "QuickPay ID:" . $callback_data->id . "<br />Type: ". ucfirst($operationData[$operRunID]->type) . "<br /> Status: ". $status_codes[$operationData[$operRunID]->qp_status_code];
$history->notified = 1;
in plugins/hikashoppayment/quickpay/quickpay.php
If you change the $history->notified = 1; to $history->notified = 0; then the customer won't be notified when the status is changed to "cancelled".
I would recommend to report the issue to quickpay so that they can have a look to the situation since they develop the plugin and they might want to include that change or some other change to take your situation into account.