This happens me too wench, when i'm at work.. most sites (ive noticed) log you out kinda automatically when you close the browser... but here it doesnt, you've actually got to click "log out" before you close it...
Sometimes if i go and use a PC i havent used in a while, i'll be automatically logged on, the only way of that not happening (i think) is just to make sure you "Log out" every time on every computer...
If you're info is still saved on the PC you were using, i honestly think the only way of that being logged out is if you go and log yourself out on that PC...
I could be wrong, but it all just seems really similar to what happens me.