Game Center mixes up scores of multiple users (apple IDs)

(New iPad, iOS6 - all apps are up to date)

My son and I both have our own Apple ID.

When we play games in Game Center, we use our OWN ACCOUNT.

Still we get each other's scores & achievements.

Example:

Subway Surfers:

I log on to GC using my credentials, play the game (one or more times).

The I log out of GC.

My son logs on to GC using his credentials.

Subway Surfer shows my score, multiplier, achievements, and upgrades.

He plays the game, logs out.

Then I log on to GC using my credentials.

The results of my son playing the game is showing in my game.

Since this is not only the case in Subway Surfers but also in a few other games, my guess it is a GC-problem more then in the specific app.

We even tried closing the app(s) & GC by double clicking the home button,

1. From the Home screen, click the Home button twice.
2. Tap and hold on the app.
3. When it starts to jiggle, tap the to close it.
4. Double-click the Home button and try opening the app again.

But this did not solve the problem.