How many orchids do you have?
If you have just a few, then manually washing the leaves down helps.
I know it sounds like a tedious work, but that's how I deal with them if I ever have them on my plant, which rarely happens but one of my tall nobile dendrobiums got some spider mites in the fall two years ago.
One thing is, spider mites (and other mites) in general indicate you are not watering your plants enough (underwatered thus stressed plants seem to have special magnetic attractions for mites) or the air is too dry.
I'm an indoor grower, so except for the summer when I leave my window open and the humidity naturally stays relatively high here in NYC, the air tends to be rather dry.
I mist my plants often and try to water all my orchids well as long as I remember or have time for them.
Then I also check the back of the leaves quite often just in case there are any mites hiding. Spider mites are easy (at least for me) to identify visually because they are much bigger than some other mites.
If intestions are bad, and even if it isn't too bad, first either wash down or wipe off them all off with water.
If possible, mist the leaves every morning.
Wash down the plant (especially the back of the leaves) with either plain water or mild soapy water every other day for a couple of weeks and that is usually the end of spider mites. The reason you need to wash them off this often is so that you get the missed ones from previous washing and the new hatchlings.
After about a couple of weeks, you manage to break the cycle and they are gone unless they are reintroduced, which they can, if you leave your window open, they can travel in easily.
Also, if you have other houseplants around, check them for the presence of mites.
I find orchids to be much more resistant in attracting bugs compared to other plants.
so check other plants if you have them near your orchids.
I had to discard one houseplants that was loaded with mites while orchids near it had none on them.
Orchids are tough, but they need care.