how can I control my puppet by phone in character animator cc

It looks like he is using an app called ROCCAT Power Grid. (He mentions it at the end of the video.) Looks like its an app that allows you to trigger things on your computer (talks about making it easier to play games without using keyboard).

The other approach I had wondered about was to use a MIDI app to send MIDI events to the computer. E.g. How to Use Your iPad as a Wireless MIDI Controller (Mac/Windows)

It did look rather cool tapping custom icons on your phone. Could be useful for live performances, especially with say an iPad where you get more screen realestate for buttons etc.