your contractor has no proper tile experience ... I would not trust him with tile work since he doesnt know the most basic concept that ALL TILE needs an underlayment when installing over a wood substrate.

It needs one of the following types of underlayments or backerboard units:

a load distribution and uncoupling membrane like Schluter Ditra,

a cement backerboard unit like Durock or Wonderboard,

or a fiberous tile backer board like Hardibacker.

as to installing over the luan and vinyl, it is also not recommended at all.

repair the damaged subfloor.

as long as its dry and solid the underlying subfloor should be ok.

you can test by poking it with a screwdrive or an awl.

tearout previous flooring.

if there are asbestos concerns with the bottom layer of resilient flooring, only go over it if it is down very solid and tight, as encapsulation and cladding is the preferred method of dealing with asbestos flooring in the home, but get rid of the top layers and the luan definately.

and you may want to hire a retailer or indepoendent flooring/tile contractor that knows how to properly install tile.

Thanks so much for your post. I was hoping I'd get a response from someone as I have been in a panic.