All your data is saved in the cloud using iCloud (iOS), Saved Games (Google Play) and WhisperSync (Amazon) so it should work seamlessly - assuming you’re signed in to one of these services and you’re on the internet.
If your data is still not coming through on a device, then you may just need to give the cloud a kick. We always sync data cautiously and will never overwrite data that means you lose progress. Go to the device with the higher score and complete a Career match to win some R - this will send fresh data up to the cloud. Now return to the other device and hopefully that new data should come down and get you back in sync.