It's possible that the mites could have hitched a ride on the rat, but reptile mites are host specific. They feed specifically on reptiles, so they wouldn't survive long on the rat's fur. It's also possible that if you were near their snakes and the snakes were infested, the mites could have hitched a ride on your clothes. I'm not sure what you're using to treat the mite outbreak, but spraying the snakes every three days sounds not only excessive, but stressful to the animals. I would recommend ordering a can of Provent-A-Mite to treat everyone. If you follow the instructions on the can, one treatment is all it should take. A second precautionary treatment after a month is recommended, but it doesn't require spraying anything on the snake, which means less stress IMO.

Good luck. Mites can be seriously tough to get rid of once they've established in your collection....