Under total utilitarianism, [most people would say that] I do count the preferences of that new person.

You only count their preferences under preference utilitarianism. I never really understood that form.

If you like having more happy people, then your utility function is higher for worlds with lots of happy people, and creating happy people makes the counter go up. If you like having happier people, but don't care how many there are, then having more people doesn't do anything.