I've read online before that it's safe to be outside during mosquito spraying so you do not have to actually stay inside when the spraying for mosquitoes is happening.
However I still stay inside because I do not like breathing in chemicals when I don't need to so I stay inside until they are finished with the mosquito spraying.
Then I was at least 30 minutes to an hour before venturing outside to allow the chemicals to settle down so that I avoid getting possibly sick.
You never really know how harmful those chemicals are and they could cause health problems even without there being proof that they could.
So I would go inside the house while they are spraying for mosquitoes and stay inside for a minimum of 30 minutes after they spray near your house for mosquitoes.