There are no rigid rules regarding timeframes suggested by your question. If the officer actually seized your vehicle he had a right to then make an inventory search of everything in it w/o a warrant. If I understand your question the issue is did he have reasonable suspicion or probable cause to seize your car and then if properly seized what was the proper scope of the inventory search.
There are no straightforward, simple answers to these questions. The police not only have a lot of power, but they also are not legally required to provide explanations to suspects for their activities. At least not until a court orders them to do so. A lawyer can contact police in a way that protects a suspect from further incriminating him or herself.