Your exterminator is incorrect; bird mites can live only on avian blood (not mammal blood), so they are going to starve to death unless they can find a bird in the next few days.Yes, they will occasionally bite humans in desperation, but our blood for some reason is not satisfactory for their survival, so they will die.  Some people develop itchy lesions at the bite site, but most hardly notice the mites, other than the annoying sensation of something crawling on the skin.  The mites are harmless to humans -- they do not transmit any disease agents.  So there is no concern about their getting on your children or other people.Do you have a feeling for where the mites are entering the living portion of the structure?  Do they seem to be coming in through cracks around the window frame?  Sealing any openings (caulk, foam-in-a-can, whatever is appropriate for the site) makes sense (and not just to prevent critters entering the home – it also reduces energy lost as the AC air seeps out).   Then I would recommend spraying around the entry area with an appropriate insecticide to neutralize any mites left behind, as your exterminator recommended.  If there is a question about which acaricide to use, I would recommend a pyrethroid.  This would be an excellent time to take a two-week vacation, if you are so inclined.  Bird mites can’t survive more than a couple of weeks without a host, so you can take your family away and just let the mites starve to death.  Reassure everyone that avian mites cannot survive on humans (or other mammals).  And do not believe a word you read on birdmites.org!  While the originators of that website are no doubt well-intentioned, the site if full of errors and outright fabrications.  You have no doubt already noticed that you can easily see these mites with the naked eye (while birdmites.org claims they are "invisible").  Do be aware that the power of suggestion is very strong; even after the mites have died off, you likely will occasionally have the sensation of mites crawling on you (our subliminal memories are apparently long-lived).  Having worked on bird mites for over 25 years, neither I nor any of my research team have ever had bird mites infest us.