It is possible that email notifications are enabled in the gateway. In the case of Authorize.net, Go Cardless, you have the option to set up notifications from your Gateway account as well.
To stop these emails from being sent to your customers, you need to disable this setting from the gateway.
GO Cardless:
If you have enabled email notifications in Go Cardless (Settings >> User Settings >> Email Notifications), uncheck the 'New Customers' and 'Alerts' option (these emails will be sent to you and not your customer). Refer to the screenshot below.
Authorize.net:
If you have enabled email notifications in Authorize.net (Account >> Settings >> Transaction Response Settings >> Email Receipts), uncheck the 'Email transaction receipt to customer' and 'Email customer for each successfully authorized ARB transaction' options.