The tire pressure monitor system in todays 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.