You are safe to pet your dog and then the snake. Mites are specific to the host.
You would have had to pick them up somewhere that had reptile.
If the mites were not that bad I wouldn't think they would have done it. But Im not going to say the didn't. I truly don't know.
It may very well be the spray. But if it is I don't think you have much to worry about. Certainly if this spray caused a large concern or harmed snakes you would be able to read about it.