When playing a game that uses the Apple Arcade iCloud to store your saves, please make sure that you are logged into your iCloud account and that your iOS device is correctly set up when you're playing.
If the setup is correct, the title will be saving your progress on the cloud and this should make your saves transferrable between devices - i.e. iPhone and iPad.
To check your configuration, please follow the steps in this official Apple article: https://support.apple.com/en-gb/HT210382