AFAIK, it was the loose pipe wrap that gave it a bad name.
That stuff would dry out, become particularized, and went airborne when disturbed.
Fiberglass, rock, or any sharp and fibrous dust are the same.
That glue dissolver will only work when in direct contact (at the edges).
I prefer a propane torch on top of the tile to soften the glue. Wait a few seconds for the heat to soak in. One fan blowing fresh air in, and another big one blowing fumes out the door.
You should watch some Holmes on Homes.
They finished a basement floor and used some neat techniques with sealants and a plastic waffle board underlayment.
Concrete soaks down heat and lets up water/radon vapor.