I hope I can provide a bit of insight.
The app must be completely closed, not just exited.
If you are closing the game by pressing the home button or using gestures on your device, the game is still in your multi-tasking bar/area and the ads will not be turned off.
In order to completely quit the game, press the Home button to exit the game, then access the multi-task bar/area by double-tapping the Home button.
(iOS 6 and below)
Press and hold the icon for the game until you see badges with a dash appear in the upper left corner of all the icons. Tap the red badge for the game, which will completely quit the game. When you open the game again, the ads will be gone.
(iOS 7)
Find the game screen in the multi-task area and make a quick upward flicking motion with your finger on the screen. This will close the game. When you open the game again, the ads will be gone.
To learn more about managing apps on your device, you can consult the User Guide for your specific device. Apple makes all of the manuals available on their site for each device family. You can find all of their manuals here:
http://support.apple.com/manuals/