"Which should I use on the corian/tile backsplash junction: silicone or water-based caulk? " If the area is silicone contaminated you likely have little choice but to use silicone, but even then you need to get the area as clean as possible. Naphtha seems to work better than other solvents. If you get the silicone level low enough new silicone caulk should work fine. Its chief drawbacks are being a PITA to apply and clean up, a limited number of colors, and it is not paintable (not an issue in this application). I have noticed a lot of poorly done tile joints lately. Wall tiles sitting tight on counters leaving no real space for caulk. Bathrooms seem to be even worse. Wall tiles so tight against the floor of the shower you can only make a large cove of caulk instead of a narrower joint that is less prone to damage from cleaning (leading to the inevitable leaks).

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.

Caulk, colored to match the rest of the grout, allows the countertop to move without cracking the grout. Which cracked because cabinets/countertops will move independent of the wall. The caulk should have been used instead of the grout in the first place. Using clear is a bandade---to negate having to remove the old cracked grout and do it right.

You want to caulk that joint, not grout it. Any change of plane, like counter to backsplash, counter to cabinets, etc. should be caulked to seal it from moisture. Caulk should remain flexible, if there is any movement in either surface. Grout used there could crack over time and you lose your moisture seal. For our last two backsplashes, I used caulk that was color matched to the grout that we used. Since our grout was sanded in both instances, we got the sanded version of the caulk. This was available at the tile store that we got the grout from. When it is all done, you should not easily notice the difference between the caulk and the grout.