How does the iPhone symbol turn off on Facebook?

On Facebook it shows a little iPhone next to person indicating that their "logged on" and i was wondering when you turn off your mobile device (iPhone) not shut down just turning it off does it remove the symbol, or does it stay there for a while and then goes off?

I'm not an expert on this but I have an iPod touch which uses the same Facebook app. I'm pretty sure that there's a separate app for Facebook messaging and you have to log out of that in order for the "mobile" symbol to go away. It doesn't matter if you're in the application or not. Again, though, not TOTALLY sure. Hope I helped!