Uninsured driver rear ended at red light

Hi there, today I was rear ended while waiting at a red light on a residential street. There is significant damage to the back of my car, I believe it’s totaled. The truck that hit me has sustained no damage at all. He was also not injured, but I hit my head on my wheel and I have whiplash. We exchanged information, but he asked me to “wait” before I report the accident because he needed to pay his insurance tomorrow (?) I’m assuming this means his insurance was not active while the accident happened. He did send me a screenshot of his insurance policy though. My insurance policy covers an uninsured driver hitting me, but I don’t have collision coverage. In the end, I reported what happened too the police and also to my insurance company. They said I could possibly get $3500. I’m not sure if that’s enough to cover the cost because my car is pretty messed up. My question is would I be able to call this guy’s insurance company to pay for the damages or should I just wait on my insurance company to pay me out? I’m not sure how this all works, it’s the first accident I’ve ever had. I am 26 years old in California. Thanks.