You must be confused on functionality. When a public user registers for an event, DT Register will NOT create a Joomla user account for them. Since no login account is created, you certainly would not ever receive a new user email.
When they register for an event, you'll receive a confirmation email that they registered for the EVENT... not the Joomla site.
So even though JS is propogating the forms? I did think that it would work the other way around also. We would like to ensure that people registering for an event have an account on our system. What do we need to do in order to make this happen?
No, it doesn't work both ways. I would recommend setting the event as Private, which will force users to create their login account before they can register for your events. You can customize the private event message, so you could include a link to the user registration.