Game progress not being synced between devices
I have an iPad 2 and iPhone 5 (iOS 6.1.3) and my game progress isn't being synced between devices. Both use the same Game Centre account and I have iCloud correctly set up on both devices. I do understand that some games don't support this feature but I have many games that definitely do yet they still don't sync. I did notice games that save data in the "Documents & Data" section do actually sync my progress between devices, but games like Cut the Rope, Where's my Water etc don't. I've tried searching online to find a fix for this issue but I can't find anything. Hopefully someone here has experienced the same thing and might be able to help, any help would be very much appreciated.
iPhone 5, iOS 6.1.3