I do Believe it is possible to play the game on two different devices, though I do not do so myself.
My understanding is also that it is important to Close the game entirely on one device Before opening it on Another.
I have mine backed up to Facebook (dummy account) so that I can play on two different devices (Ipad at home and Android Phone during my commute). 99.9% of the time it works fine switching between two devices. For reference I switch devices all the time during the work week.
Sometimes there is a syncing issue between the device and the game servers. I've had small hiccups (lost a token or two) and 1 giant one where I lost a whole hours play.
If you notice anything funny after switching devices, just contact customer service inapp and they should be able to restore your progress if you give them a thorough account of what happened.