Game Center issues with 2 accounts and 3 devices.

I have a personal iPhone 4s and iPad Air. I recently got an iPhone 6 as a company work phone. I used to have my Apple ID signed in on all 3 devices and played clash of clans on all of them. Recently I gave my young son the iPhone 4s and created his own Apple ID and game center. We then reset the iPhone 4 to remove all of my old information and gave it to him. When he downloaded clash of clans to play with me he got my clan but his Game Center showed his name when it loaded in. Is there a way that he can have his own base seperate from mine since he created his own account?

thanks in advance for any help!!