How can I stop high scores from going onto my iPad from other devices on my account ?

I have two children not old enough for their own iTunes accounts on my own account and on games like Jetpack Joyride I get their high scores and progress when I play the game . I fully understand why this happens but can I stop different devices from sharing game data . Signed out of Game Centre and uninstalled Jetpack joyride but once reinstalled it still had previous high scores.