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
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...