I don't know about a whole tank treatment, but Coral Rx Pro (and probably any similar tea tree oil based dip and likely others) should kill them pretty quickly (jump off and scrunch up.) And at least in my case, whatever eggs they may have or carry seemed to go away with the treatment - maybe they carry their young and they die if the parent does, maybe their eggs are susceptible to the same sort of dips.
If you're not sure where they are, you could try pulling some frags of different species and just seeing if they come off in a dip. If you find one with them, you know their food source, but in my case it was on a zoa frag which didn't look particularly damaged.
There's some chance they're detritivores or something relatively harmless, but I don't know of great resources to ID them to know for sure. Spiders tend to be rarer in the hobby, I think maybe a combination of them not being particularly durable and probably that a bunch of treatments kill them effectively.