To make other devices log-out from Game Center

Someone else can access the game I am playing that is called Clash Of Clans. I have been trying to find a logical answer on how that person can still have access to my game even after I change my Apple password. The explanation I came out with is that, the person who is playing the game somehow had an access to my Game Center account and as a result he can play the game just like me. Moreover, I discovered that even if you change your Apple-ID password which is your Game Center username and password at the same time, Game Center doesn't ask for the new password. Which makes the ''hacker'' of my Game Center account still accessable to my game.

I still don't know how he accessed on my Game Center account first place, but I need to find a way to log him off so that if he gets disconnected, he won't have access to my Game Center ever again.

Is it possible to log-off all devices that is connected to Game Center?

OR

Is there any way to fix my current situation?

I am really annoyed because everytime I log-in to Clash of Clans -which uses Game Center to make the game data appear on different IOS devices- I realize that someone else made changes in my game.