Do I need to add adult driver with learner’s permit to my policy?

Not sure if this is the right place to ask. My father in law immigrated to the US last year and is staying in our home. He got his learner’s permit last year and has been practicing in one of my cars while I sit in the passenger seat.

It didn’t occur to me until now, but does he need to be added to my policy while learning to drive? We are in the state of California. We have AAA insurance. The car he’s practicing in is fully paid off but we still maintain full coverage. I glossed over the policy but the jargon is a bit confusing. Im afraid to call insurance to ask because they might increase my premiums. Has anyone been in a similar situation and got into an accident?