I'll happily install them. I would rather do it myself instead of having the GC's guy/gal screw up my hard work then call me back to fix it. The tile setter has the proper diamond bits / hole saws and understands the waterproofing system used. The GC will pull out the hammer drill & masonry bit. Choose wisely. https://www.ceramictilefoundation.org/homeowners-guide-to-hiring-qualified-tile-installer

the only other way to get a diff color would be if he used an AdMixture to the grout instead of water. But it's highly unlikely. If it's normal cementious grout, he would use water from the hose. What they mean about diff colors is if you partially grout one day, and don't finish. Then the next day you come back and mix up a new bucket of grout. (using the same bag of grout). The problem is, if you don't use exactly the same amount of water, the same temp of the water, and the temp outside isn't the same as yesterdays batch of grout, that grout will slightly differ in color. But it's not going to suddenly go from white to tan! it's just that those two white shades will be slightly diff right next to each other.

No, that is not a quality job. How did you choose the tiler? Why did you separate out the materials and build tasks? Most professional tile installers would never take on a job that did that. They must control the entire process from the studs out, as well as the materials selections, in order to produce a quality result. Or to warranty anything. A typical tile install where they control nothing, and relybon someone else’s prep, would not receive any workmanship warranty, if you could find someone to accept those conditions. Frankly, it is is a red flag if they would take the job as outlined.

Where is it in the shower (pic from further back would help)? Is the stain the length of the tile? Only one corner? What kind of tile? What is the substrate behind the tile? What is the waterproofing? How was the tile set/installed?