ccrane,
None of what your saying is happening should be happening. It sounds like something else is conflicting, but I can't understand what that may be without seeing your site.
What should happen is, after the user logs in, there could be a "Welcome Alex" text (if the Greeting setting is enabled) and a Logout button. Clicking that logout button should redirect the user to the Joomla logout page. There is no popup that the SCLogin module uses, so if you're seeing one, some other plugin or extension is altering the standard logout functionality.
I hope that helps get you started,
Alex
Change text on button once user is logged in
