Really, it is not necessarily programming but rather registering the sensors. The receiver in your car, which receives the signal from the sensors needs to know which sensors to pay attention to. Otherwise it would be receiving all the TPMS sensors in traffic or parking lots. How would it know? Really by driving it around it literally forces the system to accept the ones it seems to always hear after a while. The wands, which are simply electromagnetic coils force the sensor to send out something akin to a pairing request. You can use a regular strong magnet to achieve the same result. You also need to have the vehicle in a receptive mode.

On a fun note, my own system got terminally confused yesterday. I had to transport my wife's Range Rover wheel to be repaired down to Phoenix, a 2 hour drive with the tire & rim in the back. When I re-started to go home the system now didn’t recognize any of the wheels or spare. Stayed offline for the next two hours. Got better by morning. It is an old, by tech standards, system in its design. Has its deficiencies, kind of; live & die by a bad design.