TIP extension with new Residente Temporale

Yes, with more information.

As long as you have your temporary residency, you can drive a foreign vehicle legally. You were issued a 30 day TIP because you weren't yet a temporary resident.

The catch is, in order to get your deposit back you have to return to the border and turn in the TIP. No, there is no way around it. It's a case of two different agencies that aren't communicating. Immigration issued your temporary residency, and Banjercito issues the TIPs.

So the answer is yes, you are legal to have the car here, but you will be forfeiting your deposit.