What he did probably won't bother the hardwood. The asbestos exposure is so minimal you might have higher exposure walking through a primary school built in the 70's.

Nailing through asbestos is not ideal. But it happens from time to time. My concern is the hardwood. Not all engineered hardwood floors are allowed to be glue down...but most are.

I would try to understand where the communication problem came in. I would review the contract, the wording, etc. His approach is MORE expensive (by as much as 3 times more expensive) than what you were planning to do. So....you MIGHT want to point out to him that he just cost himself hundreds, if not thousands of dollars. If you point that out, he probably won't make that mistake again.

But the main question? Yes. You are overreacting. The exposure, if any, is into the infinitesimal.

In my opinion you got a much better installation than what was planned. And I agree with Cancork in that you have absolutely nothing to be concerned about. The asbestos tile is now fully encapsulated and you can rest assured that the problem is now fully resolved.

Just to add to the excellent advice above: Asbestos is only dangerous when airborne fibers are present. Tile/shingles/adhesives containing asbestos lock the material into the product, making the possibility of fibers becoming separated almost impossible.

The more dangerous asbestos is in insulation. Inside walls, covering HVAC ducting(older systems), in wall board/ceiling tiles(older buildings) products, ceiling popcorn(pre80's versions)or loose insulation in attics(rare). Those products do not lock the material as securely and allow it to be 'friable'(able to be crushed by human hand). Friable asbestos is dangerous, but only if disturbed without proper precautions.

Although the way your installer proceeded with the new subfloor and new flooring isn't something we'd recommend doing, pulling everything up to start over would be completely worse and just unnecessary. In fact, pulling everything apart would, most likely, be the cause of the health concern you're trying to avoid. We would absolutely recommend leaving it alone at this point because, as previously posted, the asbestos is only harmful if made airborne, and inhaled. Here's a link to some useful information on a different option when asbestos is discovered in your home.

Alternative option for asbestos floors

it’s a pity that I didn’t stumble upon this thread before