Unsure if it affects parrots or dogs, but it does affect cats. I've heard of people using front line spray regarding outside the vivarium or a layer of vaseline. Just wanted to add that callington has worked miracles on ours, we tried no more mites but it done literally nothing, few days of using callington I haven't seen a single live mite (my poor guy was crawling with them) and hoping we've washed away most of the eggs.
My vivs are in the room me and my dog is in but hasn't seemed to affect him in the slightest. I wouldn't spray while he's in the room though.