I'm no guru, but here goes.....
I haven't been able to find this as being a problem elsewhere in cyberspace, although, I'm sure it must be....
On my own iPad, I have not be able to recreate the issue with popup ads, such as being described... I am using Safari.
If you haven't already, go into settings and then Safari. Scroll to where is says Block Popups and make sure that is turned on.
Back in Settings, scroll down until you find Game Center. Click on that and make sure you are NOT signed into Game Center. If you aren't signed in, it will ask you to Authenticate. Your AppleID should already be filled in. At this point, simple hit Cancel to get out of it. If you are logged into Game Center, logout and see if anything changes.
I'll keep looking, but this seems to be rather isolated.
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