In the industry "tile" means ceramic tile not vinyl composition tile (VCT) you're referring to. You're asking whether to install an underlayment (not a subfloor), and then ceramic tiles.
Chances are there is a thin (1/4") underlayment under the VCT, this needs to be removed for best results. After that we need to evaluate how the subfloor system is built to make sure it's stiff enough for tiles. (probably is). You then install a cement backer or membrane then the tiles.
BTW, if your floor was made after the early-mid '80's there is likely no asbestos.
Jaz |