With engineered joists, you would probably need to consult the manufacturer's specs to calculate the deflection of your floor, but odds are that the builder has given you building code minimum, which would not be sufficient for natural stone or slate for sure.
Couldn't find the specs for your 120 joists, but as an example, see the fancy formula on page 3 of the following document:
http://www.ilevel.com/literature/TJ-4001.pdf
I was checking the installation guidelines for Ditra, and with 24" joist spacing, they recommend adding a minimum of 3/8" of plywood plus the Ditra.
You might want to post this question for Tileman on the Mike Holmes Fan Forum.