I've done the same experiment as Saraubh using 2 browsers (chrome/firefox) and my cron jobs also run every minute, but the users stay logged on forever unless they log out.
Is there some sort of automatic timeout to log the user out automatically upon closing browser? If so, it doesn't seem to be working.
Also, on chat plugin configuration, I tried selecting "friends only" mode but in the user privacy screen, the user is still shown options to have chat available to "Everyone, Friends, Just Me". This is confusing. If chat is in "friends only" mode, they shouldn't see the option to be visible to everyone.