Toyota's TPMS system is very simple. Sensors broadcast signal, computer matches FCC IDs and checks tire pressure threshold, if its all good; its happy and the light stays off.
When you need to replace 1 TPMS unit, you must manual obtain all 4 or 5 (depending on the vehicle) FCC IDs on the vehicle; usually done by manually writing the code on the back of the sensor or using a TPMS tool to get the Hexadecimal ID. Then you program all the sensor IDs within 5 minutes using a capable scantool/TPMS programming tool.
Sensors are normally "asleep" and will not actively broadcast a signal until pinged by the TPMS module and/or tire pressure drops below roughly 28psi. You can "wake-up" a sensor by releasing pressure from the tire, usually a 6-10 psi drop in less than a minute or two will wake the sensor up, or if it drops below 28 psi, conversely a TPMS tool can also be used to "ping" the TPMS units as this is how you get their IDs.
Now that's been explained...
Assumingthe shop did not properly program all 5 TPMS IDs into the system the Tire Light will blink for about a minute or two on start-up and then go solid (indicating a fault in the system). If the light is on solid from the moment of start-up, there is a pressure related issue. I've noticed that even freshly programmed sensors will throw miscommunication codes as they seem to go back to sleep after programming, normally if just sit in the car for about 5 minutes or so after turning it on you can see each sensor wake up and provide information. If temperature or pressure show un-realistic values (i.e. -40 degress, -27 psi, stuff like that) then they are not responding.
If it turns out the sensors have been programmed properly I would have them pay to have the dealer break-down each tire and visually inspect the TPMS units for damage to prove they did not break them and provide an impartial 3rd-party to verify the work was done improperly or properly. If they do not want to pay for that, you can get the reimbursment through other methods if they will not co-operate. Bottom line, they more than likely did not program the system properly and/or were too impatient to verify proper communication; if they did that, then more than likely they damaged the sensors during replacement and are responsible.
