how long does it take to hear back about a claim?

For context, I live in WA state.

A week ago I hit a parked car while trying to park next to it. It was the first accident I got into so I was unsure of what to do, but I gave my info and moved on. I did ask if I should get anything from him, but he said no. From my perspective, I didnt cause much damage to his vehicle (a dent and a scratch) as compared to mine.

I did tell my insurance company (amfam) what happened and asked if I should open a claim of my own, but they said no unless I wanted to repair the damage to my car or I could tack it onto the claim that the other person was going to make. However it has been a week since this has happened without a word from my insurance company about a claim against me. I am wondering if this is normal as I brace myself to pay my deductible.