The Williams Pinball application can use 2 types of authentication. One is connected to your Device ID and one is connected to your Game Center/ Google account. If you are logged in through your Device ID your in-game progress is not transferable because it is connected to the device, not to your Game Center/ Google account.
You are able to change the login type the following way: Settings->Social->Log out. After you logged out the game will ask you if you would like to use Game Center or Device ID. Here you can choose between the login types. We would recommend you to choose the Game Center/ Google account option, as that way, your account will be transferable.
If you still have problems with the login types, please use the New Support Ticket option above.