Your link in the OP points to a different platform.
What URL to the MyBB forum?
PM details. I'm willing to give it a shot.
Although I will say, successful email function will depend heavily on your server. There are several stumbling blocks on the way.
MyBB forum software hands communications off to another independent component.
It sounds like MyBB is sending to the mail server, because you're getting no error messages.
Maybe the mail server is not sending them out. You'd need to look at the mail server logs.
Or, if the server is sending them out, they are not being received due to filtering for spam at hosting provider or at receiving ISP.