EPDM is fine for roofing, Neil, but not if any Portland cement-based material was applied directly over it. Known problem, that.
For a tile installation over occupied space you need a primary waterproofing layer (your EPDM), then something to protect that and provide drainage, then a properly installed mud bed, then a secondary waterproofing layer suitable for your tile installation. Schluter Systems does make the products and specifies such a system, as do others.
The only single layer waterproofing method for that installation I'm aware of is using
Noble Deck from the Noble Company. That requires
a minimum slope of 1/4" per foot in the deck framing and a layer of CBU or deck mud over the decking, as a minimum.
We'd need to see some photos of your application to comment much further. Lot of other consideration in an installation like that and a lot of liability.
My opinion; worth price charged.