Yes however you can't use the remote to start viewing. You must use the Tivo Apple IOS app; select the Mini, go to your shows, select the Amazon recording and select watch on TV. The content should start playing and at that point you can use the remote to pause, rewind and play. If you use the remote to go back to your recorded shows or back out you must go back to the Apple app to restart the show.
Search function is your friend, there are a few other threads about this.
Not sure if this by accident or design, hopefully they will fix this in the future. By fixing it meaning they will add the standard remote to play Amazon recordings and not take this away completely. It's nonsense that you have to use a apple device to do this as after all that is the whole purpose of the Mini is to not transfer protected content but to stream it from a central source.
TiVo Roamio Pro
TiVo Roamio Plus (3tb)
TiVo Mini (three)