The auto-login has a timeout feature. We set a cookie in the users browser to prevent the auto-login from occurring for the length of your Joomla session timeout (in Global Config). That counter is reset when a) an autologin occurs or b) the user clicks the logout button on Joomla. From that reset period, the auto-login will not fire for until 'session timeout' minutes later.
The reason we have the timeout is due a bug that Facebook introduced about a month ago where the autologin could repeatedly be called. Addtionally, when the user logs out of Joomla, they shouldn't be auto-logged back in, or that will completely frustrate the user who isn't able to log out.
Hope that makes sense. If you need, we can help you disable or decrease the timeout.. though I wouldn't recommend it. In 'normal' use, a user generally shouldn't be logging in and out repeatedly, though I can understand how, for testing, it can be annoying.
Thanks,
Alex