I set the Admin account to “mailto” and created a new account, then confirmed it. My Admin account didn’t get notified. Looked in Users and do see an account pending.
How did you create the new account? If you did it using “Add new user” while logged in as admin then no, you wouldn’t get an admin notification. We assume that if you did it, you would know anyway!
If you go through the full registration as a prospective new user then it should work. I get new user request every week or two and it always works fine for me. I get notified first of the request, then of the fact they have confirmed their request.