I don't know what they are using, it changes every couple of years, but I live where the area gets sprayed once a week just at the end of dusk by airplane. This goes on for three months, in the area and including right over the top of my house and beeyard. I used to think it was the cause of my hive losses, but I've proven myself wrong. If I make sure bees are well fed and medicated against mites, then my bees do fine. I'm sure the mosquito spraying has some negative effect, but if there is one, it's not nearly as noticeable as heavy varroa mite infestations and lack of good forage. And Oh, I do not do anything special with the hives on the nights they spray or the days after, nothing special or different at all.
When I first moved here the mosquitos were so bad they covered the walls in the house. I'd kill multiples of ten's every night before bed, and wake up with multiples more in the mornings. Now, nary a skeeter in the house, I'll take the mosquito sprays any time. I don't know what they have figured out and what they are using, but it's a relief to be practically mosquito free living at the edge of large rice fields in the hot summers I get here.