I started playing the game on my iPad, I’ve been trying to get the same account on my iPhone but no luck, any help appreciated.
Have your contacted Customer Support yet? (Main screen > Options > About > Support)
I actually had to get all the way through the tutorial and a bit before game center realized I already had a saved account for the game. (started with iPad, then used iPhone).
In case anyone has this problem, I got it working by signing out of my game center and then back in.