I also have a lot of springtails this year. I believe it is from all of the rain we've been having - seems like we have a storm almost every day - my lawn is still squishy wet, and it's almost the 4th of July. My water is crystal clear, CYA is 30-40-ish, FC is 4.5. They use surface tension to float on the pool water so I don't know that the chlorine is going to get them. It hasn't so far.
Some people suggest spraying the edges of the pool with soapy water, but others say soap + pool don't mix. I would guess it has to do with concentrations. I'm just hoping it stops raining for a few days and maybe the problem will take care of itself.