That is correct - they are host specific.
I keep a can of Provent-A-Mite as part of my husbandry supply kit.
My first case of mites was from a pet store girl that I picked up. I knew that they had mites, and so I pre-treated her with Reptile Relief before bringing her into my home and into QT.
Thirty days later she was soaking - the eggs that the Reptile Relief did not kill had hatched.
I always carry P.A.M with me to shows, in case I pick up any animals, I pre-treat the tub that I bring to transport them with it, and I pre-treat enclosures of all new animals with PAM.
The other time that I had mites was from a Craigslist person, and I had them in QT, but also re-treated my existing colony enclosures with PAM to make sure that I didn't accidentally carry any mites on my clothing to them.