This will depend on the laws of the state. While there may not be an affirmative obligation per se to notify the registered owner of a vehicle in your situation, it is usually done as a matter of course after the officers do their due diligence. It sounds like you the parents eventually found out about it, so I wouldn't worry about it too much.
I am not your attorney. I do not represent you. This response is submitted for informational purposes only. This is not legal advice, nor is it intended to be taken as such. Anyone considering the above referenced situation should always consult an attorney within the jurisdiction before taking any action based on this, or any other information