You can share your progress and your saves between your mobile devices (and ONLY your mobile devices) if they are with the same OS (no share between android and apple).

 

You have to be logged (GameCenter for iOS, GooglePlay Games account for Android) in game, be connected to internet and trigger a synchronisation (by opening the "Load" menu for example) to upload the datas from the device you want to send your progress to.

 

Once the dots disappear, do the same thing on the device you want to collect your progress and wait for the dots to disappear to have your all progress synchronized between devices.