Are these walls prepared properly for tile?
I'm a little concerned by the fact that "this one has had issues," but it sounds like this part of the job is being done correctly. 

Just a couple of definitions, quickly:


Drywall (aka sheetrock, plasterboard, wallboard, gypsum board) is gypsum plaster covered in paper, and is used on most walls and ceilings in dry areas.
Cement board (aka CBU) is used in wet areas like showers; drywall - even the green or blue stuff - will eventually disintegrate in wet areas.


I'm assuming that the 4" patch at the top of the shower walls is cement board, same as the lower part.

It's standard to use fiberglass tape over joints between cement board to minimize movement between the boards, and apply thinset and tile over that area as usual. You might fill the gap with a little extra thinset while tiling, but you don't use drywall mud in there since moisture will just weaken it. 

The fact that the cement boards aren't flush to each other shouldn't be a problem unless the gap is more than 1/8". Even a little more than that isn't going to cause problems, depending on the size of the tile used.

The most important thing to be aware of when a new shower is being installed is preventing water from getting into the walls. For this reason, a vapor barrier (plastic sheet) should go between cement board and the wall studs, and extend down over the lip of the shower base (or pan). This allows any water that gets into any joints between cement boards to run down into the shower base and down the drain. 

The cement board should extend down to about 1/8" above the lip of the shower base - there's no need to overlap it, since the plastic is doing so. The bottom row of tile should extend over the bottom edge of the cement board, mostly covering the lip of the shower base, then silicone caulk should be applied to seal that gap.