Carriers rate the garaging location
Premiums reflect where a vehicle is principally kept, because that is where it is exposed to theft, weather and traffic. A car insured at a parent address three states away and actually parked in Tempe is rated on the wrong place, and the difference can run either way.
A materially wrong address is a real risk
Deliberately insuring a vehicle at an address where it does not live is misrepresentation, and carriers do act on it, including by denying a claim or rescinding a policy. People fall into it without intending to, usually because a student moved and nobody updated anything.
Arizona has its own registration expectations
Establishing residency generally brings an obligation to register here, and the insurance follows the vehicle. Students and new arrivals sit in this gray zone for months without realizing both questions have answers.