Rut roh. That's not mildew. That's either plugged weepholes in the bottom of the drain, or it's a flat bottomed shower pan (the bottom of the mortar is flat, when it should be sloped) and the cement board goes all the way to the bottom of the shower pan, which is allowing water to wick up the wall. You might want to get your installer back in a hurry, because the next step is to start finding what appears to be water leaking into the immediately adjacent rooms. Guaranteed it's one of those two things. Hopefully, it's just plugged weepholes. That'd be the easiest to fix, chopping out the tile and mortar immediately around the drain, and clearing them.

Well, I'll throw out another wild one. I'm looking at those joints and they look wider than 1/8". And you said he used unsanded grout? And it appears this guy like to water his grout...I'm almost thinking that if he did a lousy job the first time around, he had problems with the unsanded shrinking during the curing. Especially if he likes water. Maybe a little flaking, a little cracking, a few pinholes opening up. Then he came back on the subsequent visit and grouted again over the existing grout to hide and fill in the blemishes. But that's just too crazy for me to speculate like that. I'm almost tempted to recommend a few ideas, mainly try a Q-tip dipped in bleach to see if the dark stuff low on the wall isn't mildew, and try a bit of an acid, even mild vinegar, on the white stuff down low on the wall to see if the white stuff is efflorescence that the acid will dissolve away. I keep coming back to your first photo: In the vertical wall-wall corner joint that is grouted, the right part of the grout joint looks like the original quartz color. the white stripe on the left part of the grout joint, as well as the white in the horizontal grout lines above the first course of tile, looks like efflorescence. The dark along the tub looks like mildew or moisture. But if the light and dark have been there forever, both efflorescence and mildew take a while to form. If your water has heavy minerals or it's heavily chlorinated, that might be a player. If is he used old bags of grout that were past their shelf life that could be an issue too. Or a contaminated mixing bucket. Or... But as you can tell, I'm just scratching my head and guessing. Does the white grout have a different texture? If you scrape the white with a fingernail, does it powder off? If it does come off, is there any of the true "quartz color" underneath it? Have you tried cleaning this grout at all? Like in my first post, I just keep leaning towards the idea that too much water was used. When I first looked at the photos of the upper walls, they looked like areas of good grout with a few blotchy dark streaks. Now I look at them and see the uniform light color being almost all efflorescence, or I'm seeing grout that has had the surface cream/pigment washed away, and the "dark blotchy areas" are actually the proper quartz color! I'd love to see this shower with my own eyes to figure it out. I probably have to take my son down to William and Mary for a college visit later this month. Bill, how about a road trip? A few crab cakes, catch a lacrosse game while we're down there, we can check out this shower all while taking my son for a college visit? Too bad the Orioles are going to be at Fenway instead of the other way around. Road trip!!! Seriously though, have you tried cleaning the grout with anything? A neutral pH cleaner and a bit of elbow...

That was going to be my question...what did he use for the mud bed. When the thickness of the mud bed gets wet, a portion of the drying occurs upwards via evaporation. You have porous grout. Minerals can be carried upwards with the moisture through the grout, and when the water evaporates, it leaves the minerals behind: efflorescence. Lime in the mortar mix could exacerbate the problem. Having the hot mopping done on a flat surface slows water movement out of the mud bed and down the drain. That is a negative too.

I don't know enough about your shower to provide positive guidance. Dark grout is usually a sign of water absorption and/or intrusion. It can sometimes show a dark grout around the perimeter of a floor, sometimes with moisture wicking up and darkening the grout in the lower walls. But that usually occurs after more than just a few showers. It can show as a dark ring around the drain. Sporadic dark spots on the floor could be due to slow draining "bird baths", or slight irregularities in what should be a nice continuous floor slope from wall to drain. Built-ins like benches can be hot spots if they were improperly detailed during construction. It's tough to say what your problem is. The typical first question is: Did they install the waterproof membrane in the shower floor on a sloped surface or was it installed directly on the flat subfloor? An overall photo of the shower might help.