The message that the other device did not save your game is caused by a number of things. If you play multiple towns on the same device, the game only caches your current playing town. When you log out and then log into the second town, the cached version does not match the version on the server. So, to allow you to go back in case it was a logout error, the message appears. Those of us who play multiple towns on the same device get this each and every switchover, and just continue. That causes the server version to be used.
If you quit the game without exiting, such as a device reboot then the game does not sync your current progress to the server. ( Sync happens on logout of origin, Krustland and friends transitions ) and the versions do not match.
I have also found the occasional server pushed or scheduled update, such as the current Gil deal will either log me out, or cause the other device message.
The sync issue is what happens when you get, for instance, more blueprints than needed at the rail yard and it doesn't register the track piece. Visiting friends or Krustyland forces a sync, and everything then matches up.