Hi,
When you manually change the order status in the backend, you have an option you need to activate to send the email notification to the customer. If you don't activate that setting, no email will be sent. This should be the same for any payment method and the payment method selected in the order shouldn't make any difference there. Please double check.
Also, it's possible there was a problem with the delivery of the email. To make sure HikaShop sent the email, please check the email history in the menu Customers>Emails history.
And what is the URL of the shop ? Could you provide it ?