Apart from a few things, the mobile app talks to the car through the internet. It goes:
Mobile app -> Tesla servers in the cloud -> Car
That means your phone needs a good internet connection and the car also needs a good internet connection, either through its LTE connection or through a wifi connection if you'Re parked somewhere where you have wifi access. The fact that the phone is in the car is irrelevant, I think. The exceptions are locking/unlocking doors, phone as key which use bluetooth le I believe.
