iPad Game accomplishments the same between devices (setting up new)?

I don't play many games on my iPad. It's usually just Real Racing 3. My kids have a bunch of games that they play though. When I went from the iPad 4 to the Air 2, I backed up the 4 and then set up the 2 from that. Everything was the same including game progress. Just a different device. I got each of my kids an iPad for Christmas. I'm going to set each of them up with their own iCloud account and then attach them to my iTunes account so they can have all of the games that they are currently playing. I know that I can manually pick the games that I want to install instead of doing a full backup. When the game is installed, will it be with the current game progress? And if they go from playing the game on their iPad to doing it on mine for some reason, will the game progress be the same? I'm trying to figure out how they sync so the progress is the same on all of the devices.

Before I posted this I checked Real Racing 3 on my iPhone. The progress isn't the same as on my iPad. But I noticed that I get a Game Center welcome on that and not on the iPad so it might just be the way that they are set up.

Thank you!

I called Apple to see what they can tell me. I can attach their iPads to my iTunes account to download the games and get them to their current levels but the games won't update. They will progress but that's it. The better thing to do will be to just start from scratch. They will be more than happy with getting their own iPads so they might not mind starting over.