I don't think you have grounds to withhold payment, unless you can find in a technical manual somewhere that thinset MUST be used to install underlayment in your State. Possibly he used a good grade of construction adhesive, or no adhesive at all and a million screws. Either way may not have been what another tileguy would have done, but may be perfectly sufficient for your circumstances. Unless you have a specific problem, you ought to pay the contractor.
I remember a customer who was terrible about paying the contractors working there. One day she casually told me about a vacation home they had that they had hired out a bunch of work to contractors to remodel the place. She said soon after it was done, it burned to the ground and they never found out why............I wondered to myself who she didn't pay...
thetiler