Just make sure you follow the instructions on the bottle for treating the birds directly if you're going to use it on the birds. There's very different concentrations to use on different animals and on surfaces.
You should let the spray dry before putting the chickens in but it's understandable if you don't have anywhere to put them. Just make sure there isn't standing puddles of spray on the floor. I ended up getting a one and a half gallon sprayer from Tractor Supply for $10 that worked really well...
This is a link to a thread I made about mites. One of the replies has a link about identifying what kind of mites they are which will help you find out how to kill them.
https://www.backyardchickens.com/threads/mites.1197698/#post-18953063
I used poultry dust on the birds and Permethrin 10%...