I don't know about tires, but typically the arcade cars are set up exactly the way they are when you buy or win one, except you can't adjust anything.
ASM and TCS are full on, and on the race cars tires are usually T5s. The dampers will be set to generic 7s and the swaybars to generic 3s.
If you are trying to practice using your prize car, go to the Change Parts screen, highlight the Race Suspension, and press X, possibly twice. This will return the suspension to stock settings so they match the arcade car. You can also do that with transmission, brakes, etc.
Welcome to GTP!
