Hi,
When you use the HikaShop registration, then it's HikaShop sending its new user account email notification.
When you use Joomla's registration, then it's Joomla sending its new user account email notification.
I know that AcyMailing has something to override Joomla's emails, including Joomla's new user account email notification.
And I also know that AcyMailing has something to override some of the emails of HikaShop.
However, I don't know if what they did also support the new user account email notification of HikaShop.
On our end, all the emails are sent the same way. The same plugin triggers are called, and we use Joomla's JMail library to send the emails.
So if the other notifications of HikaShop are overridden but not this one, I believe that it would mean that AcyMailing's override system doesn't support this one, or maybe they have a bug in the way they catch the email sending.
I don't know how that override system was done. So I can only say that. AcyMailing support should be able to answer you about these better than us since they are the ones who developed that override system. I would recommend insisting with their support.