Always caulk any changes in plane. So because your granite and backsplash change planes (from horizontal to vertical), you need to caulk rather than grout. (The same goes for any corners where you've changed planes -- such as where two walls meet at a 90 degree angle.) This allows for movement of the surfaces without cracking. You can get sanded caulk which matches grout and so it should not be noticeable that it's caulk not grout. I would certainly defer to a tile and/or granite expert, but unless the tiles are meant to butt directly up against each other, you should at least follow the minimum grout joint width requirement of the tile. This allows the caulk to get between the tiles and isolate any movement of either surface and also allows for any variations in the tile or granite. Stand up to your tile installer and insist. If he has a problem with it, you can do the caulking yourself. Just make certain to mask (with tape) the granite and the tile before caulking to protect your investment. (Nothing worse than having to clear smeared caulk off a new surface.) In my (minimal) experience it would be easier to just smoosh grout into every crevice since then you don't have to be as careful, but it is the wrong thing to do. In my opinion, either the installer is unaware (maybe inexperienced? or just improperly educated on grouting?) or is simply being lazy. This is your home and your investment and the installer needs to respect that.

I have had nothing but problems with my CAULKED grout at the base of my backsplash, where it meets the quartz countertop. It repeatedly cracks. I have had the contractor come back in and redo this area multiple times. I will no longer allow the tile company he brought in to do the job because they were so awful. Despite their brag of being in the business for years, their grout guy used regular grout at the backsplash base. Then they sent in another guy to cut it out and replace it with caulk. Despite this, it continually cracks. Every time the base cracks my contractor tells me this is movement in our 30 yr old home. My prior backsplash and counter, which was ALL tile ALL grout never had this issue. I have to pay the contractor to fix the seam every few months. Can anyone tell me why this is happening and how to remedy it? It’s really bad. The cracks are the biggest I have seen yet.

If you google, you can buy custom cut tempered glass relatively inexpensively. Or, if it fits, check out IKEA tempered glass tops/shelves. Many of their dressers, credenzas, tables offer tempered glass tops.

You place a continuous shim the thickness of the grout lines on the leveled countertop and tile on top of it. Grout the splash, pull the shim, and pump the gap full of 100% silicone color matched to the grout. Spray it with Windex, spit on your finger, and tool it to perfection. Wipe off the Windex overspray before it dries without touching the fresh caulk. That bead will flex with building movement, look good for years, and is replaceable if need be. The pictured gap between the deck and tile is too small; it may never behave or look right even after the grout is replaced with silicone.