Back to basics
So when you execute the TPMS learn function via the menu, is it actually entering the learn.
On some Vx's, when in learn mode it flashes the indicator adjacent to the wheel which it is looking to learn, you then use the tool you have to provoke the appropriate sensor into transmitting its ID code (by holding it to the tyre wall near the sensor).
It should then do a short pip on the horn before flashing the next indicator adjacent to the next sensor to learn, you repeat until the are all learnt.
The tool you have does nothing more than make the sensor talk to the system.
Its worth checking you have no cheap gadgets which work, or could interfere, with the TPMS systems installed and working on the car.
I did speak to our TPMS team, our system works by monitoring the wheel rpm via the ABS sensors and correlating it with that from the sensors. The wheel speed changes for each wheel when cornering, the first drive cycle does the learn, the second a check and then it is stored and activated mid drive cycle.