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Yes, that’s what is supposed to happen in Django. Whether you log in using the admin site or your own LoginForm, it’s the same. The admin is just an app that only some users can use. In fact, you can log in as a user that has admin privileges (such as the superuser) using your regular LoginForm, and then you’ll see that when you go to the admin, it will open automatically without logging in, because you already have logged in.
However, you can login to the admin on one window, and then open up a private window, and each one of those can be a different login. And if you need to test multiple users at the same time you can try Ghostery Browser, an extension for Firefox, or Ghost Browser, and there are others, specifically made so you can test multiple users without having to constantly log in an out.