The tiles were attached to concrete or possibly a terrazo, so the white powder is not doubt a salt or lime (efflorescence) leached from the cememnt. See for yourself, put some water with a small amount of vinegar on the powder residue. If it dissoves, it was not mineral fiber (asbestos). Any asbestos is locked up in the asphalt matrix and would be extremely difficult to separate. That is why this material, even during removal, poses a minimal hazard.