If it was a 4" backsplash then probably not an issue except that in either case, the countertop would need to go in first. And typical rule of thumb is backsplash goes in last after cabinets and countertop. Suggest you partner with countertop guy for his input/approval.

Your upper cabinets go to the ceiling, with a crown trim. A"MISTAKE'? would be resolved with a scribe of trim to that ceiling, and all that is true, level not level, should have been resolve prior to this.

OR?

Your cabinet installer is not as great as need be, or he knows and does not trust your solid surface fabricator. Which?

Routine, is backsplash LAST. Matters not what height, what material. In solid surface, this is a function of a laser template, and accuracy. no different than if it were a top on a vanity in a niche! It's done every single day with no issue by quality fabricators.

Your question is who do you trust and to what level? Have the conversation with the fabricator.

The mistake is that some of upper cabinets need to be re ordered bc the stiles are off in bar area and by fridge and there is some damage. I believe the cabinet guy wants the fabricator to put full height backsplash first so he has time to reorder cabinets. My counter top fabricator/ installer is not use to doing it this way. He does it after cabinets are installed. Cabinet guy called my countertop company trying to pressure him to do it this way. But to answer your question, I trust countertop company more than cabinet people. I also don’t want to compound errors by doing something out of order that could make my backsplash not look seamless. So, I am trying to see what is industry standard for full height backsplash and to educate myself enought to advocate for how I want it done

The 'full height' usually refers to taking the backsplash to the ceiling. Your drawing doesn't show it going up the sides of the uppers. Is there an area where the backsplash does go to the ceiling? Is this a slab splash?

Industry STANDARD is backsplash LAST.

You have one picture.

Is this above the only area of concern? Where is the rest of the kitchen plan?

Matters not. Answer is same.....Get the contractor, the fabricator, the cabinet installer all on the site, and hammer out exactly what the issue is.

If it nothing more than cabinet replacement and a timing issue" You W.A.I.T. for the full height backsplash in this area, and it delays a final finish. All cabinetry installed. Tops go on, and back splash last.

If it were a case of behind a cook top/ hood. to the ceiling....a different scenario would involve venting how what where and all else.

More and more fabricators are demanding to go first, after bases, for full height splashes, because of unreasonable expectations from clients about no gaps. Backsplash last is guaranteed to have small space between it and the uppers because the thickness of the counter in the swing up with be an obstacle. You have to cut it into multiple pieces, for logistics sake, and even if the material is one continuous piece, you get a kerf's width cut out, and a seam, which seems to make people coocoo for cocoa puffs, as they hire the cheap guys and try to bully them into better work than they are capable of doing.

Your installer does the cabinets first then the backsplash is is made to fit the space exactly that is the order regardless of what your cabinet installer wants As for unlevel items that should have been resolved long before cabinet install . Your counter people are right the backsplash can then be templated just like the counter to allow a tiny space for install filled with abead you will never see,

If some of the cabinets were damaged and have to be re-ordered the project is delayed. You still need all the lower cabinets in place before putting the countertops on and you need the uppers in place before adding a full height backsplash so that you can be assured that the backsplash goes from the counter to the lower edge of the cabinets.

Not sure I would want a full thickness slab sticking out past the upper cabinet?

Are there finished side panels on the lower and upper cabinets? Or is just a basic thin color matched skin/thin panel?

My end panels (upper and lower) that match the door/drawer fronts. Also made slightly deeper to cover the side edge of drawers/doors, for a clean look from the side.

The lower cabinets are in. The upper cabinets are the ones with the errors. The installer prefers to template with upper cabinets installed. However, the cabinet maker is trying to convince him to do it the other way around. I want to do it the way industry standard is done since these counters are expensive and we can't afford a big screw up

Does not change the answer.

Your fabricator is right, your cabinet installer is wrong, and you are the designer/contractor, chief of the show.

Get someone ELSE to install the cabinetry.

Stop fighting, just tell the cabinet maker that you will allow the backsplash to be installed prior to the cabinets with the understanding that this is per the cabinet makers request and the cabinet maker will take full responsibility for replacing the backsplash (all materials and labor costs) if the backsplash and cabinet are not aligned leaving no more than a 1/8th inch gap between the two. You will need that in writing before the backsplash is installed.

Usually the uppers go in first too. So big mistake all around.

Install cabinets first! no question

Cabinet installation goes first and backsplash is after.