There is no indication he used a cell phone at all. It says it is direct DI recording plus a voice over microphone. So I guess it is something else. A combination of both things.
But you can use your phone. While tracking drums for example I have put my phone in the overhead position and simply used the voice recorder. It generates a standard type of file that can be dragged into your software. Being digital and all it should line up pretty well. It will have a crushed type of sound to it which when added in behind the close mics can introduce a nice ambience to the sound though.
Don't think you will get a plugin to do that exact same thing.
I had a similar drum machine to that. It was a Rhythm Ace and had a very similar sound and beats to it too.