I believe they are correct.

generally the 12 inch tiles are not asbestos. The 9 inch tiles generally are asbestos. BUT #1 - encapsulation, such as tiling over asbestos, is an accepted practice. BUT #2 - Unless the asbestos gets airborne from grinding or sanding, it isn't hazardous. Simply picking up the loose tiles and shoving them into a trash bag will have zero effect on your health, aside from lugging the weight of the bag around.

FWIW, flooding the floor is an easy method of removing old, stuck down tiles.

thank you. so are the tiles that are wet need to be removed? our contractor says yes due to what can "grow" under the tile.

Most of the 9x9 format tiles were asphalt asbestos. Most early 12x12 format tiles were vinyl asbestos. Apparently your contractor believes that water has seeped between the tiles by capillary action. Over what substrate are the tiles installed? If concrete, no reason to remove them at all.

Well, if they are loose they need to be removed. And it does need to dry out.