TPMS trouble

OK, so, here is what he had to say:

He is a mechanic at a tire shop. He does their high end stuff (major engine work on commerical clients stuff, more complex work on individual customers cars and trucks). I had them swap out my OEM wheels and tires for Ray 10s and Nitto Ridge Grapplers (all 4 wheels). Later, they did a rotation. He didn't do any of this stuff himself (while his colleague was handling my wheel and tire swap, for instance, he was changing out my suspension).

He has now talked to the kid in the shop who switched out my wheels and tires and then later did the rotation to confirm his recollection. My truck did not have a TPMS in the spare when they did the switch. The kid installed a Toyota TPMS in the Ray 10/Nitto with no TPMS. On both initial install and rotation the kid used some device that tells the truck the ID of the 4 TPMSs it needs to be looking out for and at which wheel position.

The kid is surprised that the reset didn't pick up the TPMSs, though had it done so it may have made the mistake of catching the spare (you can always tell by whether the tire pressure of one of them doesn't move as you drive). He also said that in the TPMS department they have more trouble with Toyotas than any other make (TPMS sensor failures are common and in many cases getting the vehicle to recognize a new TPMS arrangement involves weird tricks outside of the official Toyota methods). So my friend is going to bring the tool home this evening but I may just buy one.

That last part (Toyota problems with TPMS) rings true to me. We have a Camry and the TPMS warning light went off around the 2nd year we had it (we have now had it 13 years) and never went off. The dealership eventually replaced EVERYTHING related to the TPMS and it still doesn't work. And my parents have had non-stop problems with the TPMS on their Prius.

So, TL/DR bottom line:
1. My truck may eventually learn the new rotation;
2. I'll never know because he is bringing a device to force a reprogram
3. I just need to buy the device.