It depends on the kind of mite. if it's a predatory or parasitic mite it needs either prey or a host to live. if its a fungus mite it will eat whatever fungus/mold it can find. unless you know what kind you're dealing with the best answer you will get will be completely vague. unless there is food and the other environmental factors it needs to live and reproduce are in place the chances of them infesting your house are pretty small.
Unless they're ON the tarantula, they are harmless. Just let things dry out if you don't like looking at them. There is no reason to buy predacious species, as they'll just come back once all the predators have starved themselves off.
As for PILES of mites, those are probably grain mites, for those you remove the food they're feeding on and let things dry down a bit.