Tire Pressure Bands

Should the system check show whether or not the tire pressure is OK? Or is it just a warning lamp on the dash? The car had 20" rims when I bought and I've had to take it back twice to the dealership for vibrations and pull at 50+ miles an hour. When I took it in the first time they had to break down all the wheels and tires because the sensor bands were rolling around inside the tire throwing the balance off. The second time they claimed there was nothing wrong. The third time I complained they sent me to the wheel shop that sold them the tires claiming it was a bad tire.

The shop said they never removed the tabs and they took care of it. It rides alot smoother now, no vibration or pull. When I bought the car I thought it displayed the "Tire Pressure OK" on the display? Maybe I'm just paranoid but I have very little faith in the dealership here. Thanks for your help
 
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