He may be getting flea bites. The fleas don't live on him, they have already bitten him and this is the reaction.
A couple yrs ago, I went to visit my brother who has a lot of dogs and 3 inside dogs. My daughter was playing with the dogs.
A day after we got back to TX, she had what appeared to be mosquito bites on her legs and I had nothing. SO I assumed much like you did. I knew bed bugs were out of the question, we too had new bedding, etc.
I took her to the pedi and I was told that she had a reaction to flea bites. I was surprised because I had no bites, my brother's kids had no bites. Dr. said that brother and his family were immune to the fleas. However, daughter was not. She also said that new bites could appear on her for up to 2 weeks. Within a week, all bites were gone and NOPE I am NOT going back to brother's house in AL.