Actually, I don't think you can switch out of the game for extended periods ... it has to be visible on the screen. @philippe's post is right on - all the calculations/physics for your flight are done on your tablet. iOS, if my memory serves, will suspend activities of an app that is not displayed on the screen after a short, arbitrary period of time. Your app can ask for more time, but typically not more than few mins or so - and less if you have a lot of other apps open - (with the exception of playing music/video, voip, location tracking, and a few other exceptions). Keep it going much longer and iOS likely force the game to crash, not to mention that apple will probably reject your app during review. Android is a little more lenient, but I'm not quite as familiar with android behavior.
Basically, unlike on a desktop or laptop, once you minimize or hide an app, it can't do much until you bring it back into view.
So in short, you can't keep the simulation going without it being on your screen - though you don't have to constantly interact with it.
As Philippe said, the only way to let you be away from keys is to do all those calculations/physics on FDS servers, in which case they'd have to buy a lot lot more server capacity - which would make the game a lot more expensive.