This is what I've been able to ascertain on Chrysler Jeep's TPMS system. The sensors have a unique ID or serial number, that the system registers the sensors by. That unique ID is at each position. So if the system recognizes new ID's, or positions of existing ID's have changed, (tire rotation), it goes into a mode to re-register the ID's. It's a process of elimination, and one of the things it's doing is making sure its not accidentally registering ID from sensors in the vehicle that is parked next to your vehicle, or one that is just driving by at that moment. It can re-register the sensors at new positions, or brand new sensors in as little as 10 feet of driving, or as much 10 miles. In some rare cases, even more.
The sensors themselves are activated by motion. So while you're parked the sensors do go into a, "sleep mode". When you start driving they, "wake up" and start reporting. And they only report every 15 seconds or so. When your tires heat up while driving, you'll notice the pressure change reported. It will ripple through the display one after the other, with a good 10 seconds or more in between. They all just don't change at the same time. The TPMS is always monitoring the tire pressure while your driving, not just when you pull up the display. If the tire pressure drops to an unsafe, under inflated level, it may take a few seconds, but you'll get the warning lamp for tire pressure on the dash, despite not having the display up at the moment.
If you drive with the tire pressure display up and running on the dash, it does not wear out the batteries any faster, because the system is always reporting once the vehicle is put into motion. It's all pretty remarkable technology when you think about it. Especially when you factor in how little it costs in relation to the amount of information it is giving you.
Now I have to research the TPMS system in my Toyota. I'm guessing it's very similar to the system Chrysler Jeep uses, because it operates identically, and gives the same information in the same manner.