How do you know when these conditions are satisfied? My subaru manual only says that the system will recognize if the sensor is missing by flashing the
TMPS light on the dashboard .
There are two types of TPMS systems that use transmitting pressure sensors in the wheels.
The simplest system looks for 4 transmitters to exist, and each transmitter must report that it senses pressure over some minimum. It is not an exact sytem, just a go/no-go guide. If one or more sensors report pressure below the minimum, then a light gets turned on. Doesn't tell you which wheel(s), just that 1 or more are low. If it senses less than 4 transmitters, then it alerts the user to an error, like flashing the light.
So in the case of your Subaru, if the wheel was taken off the car to be worked on, then put back on, with enough air in the tire, then the system should see 4 transmitters reporting pressure above the minimum. That would verify that the transmitter in the wheel under repair was not damaged.
The fancier TPMS system has digital display locations for each tire, that read the actual pressure. So by looking at the display, the driver sees 4 sets of data: LF pressure, RF pressure, LR pressure, and RR pressure.
If these tires were then rotated around to even tread wear, then the data would appear in the wrong place, e.g., the dash display location for LF is actually now displaying the pressure in the tire that is now on the RR. So a reset/training procedure needs to be followed to retrain the dashboard system as to where each unique transmitter(wheel) ID really is.
It also says when a tire is replaced, adjustments are necessary to ensure continued normal operation of the TMPS. I had a flat tire repaired. When the manual talks about a tire being replaced , do they mean a different tire being installed or do they mean even the same tire being reinstalled?
That is probably a blanket statement about the system with respect to reset or training for a new sensor.
In both of these TPMS types, the dash system has been programmed to recognize 4 unique transmitter ID's, to avoid reading a car next to yours' wheels. So if a damaged sensor is replaced, the car needs to be retrained as to what sensor ID's it now has to look for.