The tire pressure monitor system in today's cars use a radio frequency (RF) transmitter ( Tire Pressure Sensor ) in each wheel valve stem to relay pressure information to the module. The Service Tire Pressure Monitor System light / warning means there is a problem in the system, not a low tire.
The Low tire pressure warning would come on for a low tire.
The system would need to be scanned for codes if the service monitor system warning comes on.
After a tire rotation, the tire positions need to be relearned in order for the system to tell you which tire is low. A special procedure and tool is need to do this. The sensor is mounted inside the wheel, and is part of the valve stem. The tire needs to come off the wheel to replace it.