Every TPMS system is different. The one thing they have in common is that per government the sensors must last a minimum of 10 years (it's funny I know).
To accomplish this feat running on batteries the sensors fall asleep when not in use. This usually means driving above 10 to 15 mph before they wake up and transmit a reading. The TPMS sensors contain an accelerometer that wakes them up when they sense the appropriate motion. Also a rapid change in pressure wakes the sensors up. When you first start driving the sensors will usually get awoken as soon as you exceed a particular speed, again every vehicle is different.
When you install new sensors, assuming your car can relearn them by itself (some need to be programmed). The car will take some time to learn the sensors. The car will see that a new set of sensor IDs are following the car and the old ones are not present. This condition triggers a learn event. After some time, to eliminate accidentally learning the sensor of the car next to you, the car will accept the new ID numbers.
