Concrete – Did the contractor installed the new layer of cement flooring correctly

Portland Cement has poor adhesive qualities by itself, which is why it is commonly mixed with a polymer. By definition, "thin-set" refers to an application thickness of under 3/16th of an inch. Other common additives to thin-sets are water retaining compounds that help them retain moisture to extend the curing time for more strength. By adding additional Portland Cement, both of these properties have been compromised in the mix. As far as curing goes, the ANSI spec for thin-set performance specifies a final set time of under 4 hours (this link has a good run-down). Tiles should be difficult to peel off within an hour.

That said, there are several other issues I can pick out from your pictures:

• Even if the tile does adhere properly, the grout will most likely start cracking within the first couple of months. There shouldn't be any of the huge voids visible in the bottom two pictures, especially in the corners. When you float grout in, there won't be anything to support it in places other than the sides of the tiles themselves and any minimal keying from packing it into the joints.
• In the top picture, it appears that the float-cement backing was applied over sheet rock or plaster? If this is the case, it will wick moisture into the wall. Although this will be a fairly small amount, eventually it will start bubbling around the edge.
• Weight. This installation will weigh approximately 20 pounds per square foot more than another backing type. On a small shower, you're talking close to a ton of excess weight. If this is on a framed floor, it will deflect and exacerbate all of the other issues.
• I don't see any indication that any structural support was incorporated into the float-cement (wire mesh, fiberglass mat, etc.), and certainly not in the "thin"-set. This means that it will be prone to cracking over time.

I think @DMoore hit the nail on the head with this one. You need to have this contractor stop work immediately. The simple fact that he can't lay tile straight (and isn't using spacers) is fire-able in my book sub-strait aside - now you're talking about what you will see when it's done. Schedule a time for a building inspector to come by and take a look at it (you did get a permit, right?) - they are generally less busy this time of the year, so will be a lot more willing to give you a good opinion. Tell them that you are concerned that the work being performed isn't up to code and that you'd like somebody to take a look before it gets covered up.

As far as how I would go about an installation like this, I would generally back everything with framing and half inch cement-board. If I was worried about deflection at all, I would thin-set a second layer of cement-board to the first layer with staggered joints. I haven't seen a shower around my neck of the woods done with float-cement backing that was installed more recently than about 1960. Even though the materials cost more, if I'm billing $40 to $50 an hour for labor it still costs half as much overall, doesn't have long down times for curing, and is a ton easier to work with.

Concrete slabs crack. Period. For this reason, "control joints" are often cut or tooled into slabs where aesthetics are a concern. They encourage cracks to occur along straight lines where they create less of a visual blemish and can better be accommodated by expansion joints in rigid flooring.

In your case, it's not likely a concern.