The orange material that is featured in these pictures is actually the tile underlayment.  It is called Ditra Matting and is made by a company called Schluter Industries.  We have been using Ditra Matting and other wonderful products by Schluter for many years. This underlayment is simply the best in the business.  Schluter-DITRA is a polyethylene membrane with a grid structure of square cavities, each cut back in a dovetail configuration, and an anchoring fleece laminated to it's underside.  This particular underlayment is only 1/8" thick and is bonded to the substrate using thin-set mortar.

The anchoring fleece on the underside of Schluter-DITRA is fully engaged in the mortar to provide a mechanical bond to the substrate.  Our tile is then installed over Schluter-DITRA using the thin-bed method in such a way that the mortar becomes mechanically anchored in the square, cutback cavities of the Schluter-DITRA matting. The subfloor is then free to move (expand and contract) without effecting the underlayment or more importantly the tile and grout above that it is bonded to.