Hi,
To check whether the emails are sent by HikaShop or not, you need to go in the menu Customers>Email history.
There, if you see the email but you don't receive in your mail box, it means that there is an issue with your email server.
For example, it could be flagged as a spammer by some receiver email servers. You should test your emails with
www.mail-tester.com/
Now one thing I can say for sure:
If you have configured your Joomla to send an activation email during the registration, HikaShop will send the email 100% of the time. If you don't receive some of the activation emails from HikaShop, then it's not a problem at the HikaShop level.