I'm not knowledgeable enough to answer your questions, but I'm looking at that uneven vertical space and wondering why they didn't use spacers on the verticals. I thought you were supposed to space horizontally and vertically.

That edging wouldn't look so bad if it was the same color as the tile. It looks too white. Hopefully the tile store will have some type of matching trim or edge pieces. If they dont couldn't you just have a grout line instead of the plastic. That would probably look better.

Rather than use a bull nose tile, he used what a product by Schutler. The product has it's place, but not for your finish. It also comes in a dozen colors. Plastic doesn't work for me with your wonderful tile. Plus if you look at it in the store (HD carries it), there are a lot of damaged ones. Easy to crack or break a piece out of.

I would have the installer get rid of that and use correct edging tiles. The trim used goes under the tile from 1-3 ". It is a cheap option. Removing this will mean he has to cut tile again, you should get a tile trim wanted while the current tile needs cutting. If it stays as is, a sealant is needed both on top of the tiles' edge as well as the existing trim which will add to the plastic look.

Those edges, both horizontal and vertical, are best done with bullnose edge tiles.
Check with your tile supplier to see if they're available.

I'd use tile quarter-rounds for the nicest finish on that edge, or replace the end field pieces with bullnosed pieces. I'm guessing bullnoses aren't made for your decorative tiles, so that may not work - in which case, stick with the quarter-rounds. I'm not fond of the way the long rigid plastic edge just accentuates any issues with the (natural and normal) slightly-off-kilter edge of the cut tile.

Alternately, don't use any edging at all and end with a cleanly wiped grout edge; works as well as anything and looks just fine.

Thanks for all the advice. I think I like the bullnose or quarter round options best. We weren't trying to call attention to the end. We just wanted it to look natural.

I just got back from the ceramics store. They are going to call the manufacturer on Monday to see if they have a bullnose option. The other option they are looking into what the catalog calls a box liner. It would run vertical and be a little taller than the other tile. The ceramics store thought that could be applied after the rest is complete. I'll email to ask about a quarter round option too to see if that could be done the same way.

Fortunately, the installer has only glued the tiles to the back at this point. It's not ideal but at least the grout / sealer isn't on yet.

Thanks again for all the advice. Since time is short, I appreciate that I'll have some options to discuss with our remodeler on Monday.

Our tile was Home Depot no-name, but we loved it. There was no trim tile that matched and we had two walls where it would end mid-wall.
Fortunately it was white all the way through.

We painted the walls a very similar color to the backsplash and purchased caulk that was the same color as the grout. The contractor made sure to do a really straight cut and applied the caulk to the sides. It was just one of those details I wasn't going to freak out about.

My photo has a shadow so you can't see the grout, but it looks fine.