The Discount Tires/America experience leads to questions about the TPMS when the tires are rotated

I was surprised when I was barely out of the parking lot when the TPMS low pressure warning came on. Turns out they only inflated one of the tires to 15 psi. According to the TPMS, the rear driver’s side tire was low, but it was actually the front passenger’s tire that was underinflated. They fixed the inflation problem and reprogrammed the sensors, but I never would have known there was a problem with the sensors except for the flat tire in the “wrong” place.

This raises the question of tire rotation. Does Subaru (or other service centers) reprogram the position, does the car automatically change the position and I haven’t waited long enough, or am I driving around with the sensors reporting the pressure in the wrong place when I rotate the tires?

Thank you!