I spent a whole lot of time answering you twice. If you read what I wrote, you'll see that millions of people with casual exposure to asbestos live long and fruitful lives....and some don't. You'll also see that EVERYONE who is alive, babies as well as adults, has already been exposed to the stuff, so, it's always possible that you or your husband could get sick from asbestos, but I doubt you've been exposed because he was cutting on a 1990 house. I can't guarantee that neither of you will ever get sick though because you'd both had been exposed long before he ever cut into your house. We all have been.
Understand that it is alleged by the medical people that it takes about 20 to 25 years for asbestos exposure to metastasize in humans. So, even if something in your house contained asbestos and you or your husband were exposed to it, there is no way that anyone a quarter of a century from now will be able to discern whether the asbestos either of you were exposed to came from the same source, came from driving down the highway, came from your home or a former home, or anyplace in particular because of the passage of time. All they would be able to do is make a diagnosis of asbestos exposure.
So, fretting about this now is pointless and frankly, kind of foolish since it is after-the-fact and even if he, or you, have breathed it in there is no way to get it out of your lungs. It would be there to stay, period. Worrying about whether you'll ever get sick and die from asbestos exposure is kind of like worrying whether you'll ever be struck and killed by lightning or stomped on and killed by a hippopotamus.
Any of us will be happy to answer any other questions about a home that we can, but re. this asbestos thing, I'm done. If none of us has managed to quell your fears, I'm sorry, but please stop beating this dead horse.
I like Jim's suggestions. He's right, in our climate you don't want it airtight on the underside - just pretty tight so any vapor diffusion that finds it's way into that space can dissipate. The only improvement I might try to make with that is to use two-inch-thick EPS placed against the underside of the floor before adding unfaced batting. Just trim it carefully so it's a light press fit, add the batting and then the covering. Don't seal the perimeter of the foam, you want to allow diffusion to continue to move naturally toward the colder underside of the space and escape.
hausdok's post in Siding t11 or masonite was marked as the answer