First, you should consider using at least an 18x18 tile.
12x12's became outdated here in Florida at least 7 years
ago. Porcelain tile also is superior to ordinary ceramic,
and available in great styles and finishes. It only costs
fifty cents a foot more here in Florida for Porcelain.

Secondly consider using hardibackerboard rather than
cementboard, installed with strong exterior grade
1 5/8" screws and glued tightly to existing floor. I would
also use a studfinder and find the floor joists and screw
the existing flooring tightly to the joists.

The hardibackerboard should (must) be dampened with
water prior to applying thinset, and don't compromise on
thinset...buy the best multi-flex thinset you can buy. No
sense using $50 worth of cheaper thinset when $150 will
buy you the very best and provide a far superior bond.

All this may seem like overkill, but it is what insures a
long lasting bond.

The price seems reasonable for a genuine professional,
but I would question why he/she didn't persuade you to
upgrade to a modern tile, and insist on providing the
setting materials. I would never let a customer provide
setting materials since they are the most important key
to a good job- but that's me..

thetiler