Your experience suggests the joists aren't engineered to support the anticipated weight without acceptable deflection. And the backsplash is installed after the counters are down. So any settling time should happen before the backsplash goes on. Templating is to the wall. Cabinet movement should be shimmed to be level under load.

@dan1888 When the bathroom countertops were done, they templated for the countertop and backspash at the same time, and installed at the same time. They didn't template the countertop, install them, and then template for the backsplash. Could that be part of the issue?

Yes. Is your backsplash a single piece of material? Or single counter to ceiling pieces. that's about the only time I can think of for a template. I think you could cure the bath problem by shimming the cabinet.. For the kitchen, if you're using a single piece of material for the backsplash I'd wait to template as you suggest after the counter install.

If your cabinets need to "settle" after installation, most likely the installation is defective.

We had a kitchen wall that bowed in and out with the seasons, opening and closing a 3/8" gap behind the granite backsplash. No amount of "settling" would have helped. I don't think "settling" is actually a thing. If the weight load of a kitchen cabinet and countertop is bowing the floor I'd worry that the building is about to come down. 40 psf is the code minimum rating for floors, a cabinet and thick stone top can't be but 10 at most.

You don't mention how big your bathroom gap is. A little one is pretty normal--that's why it's standard to use a flexible caulk where you have a change of planes instead of grout (if tile) or other inflexible stuff.

I was called to do repairs at a home with out of level countertops. I thought the installer was a hack until I realized it was me. I was employed by a solid surface fabricator and this was new construction. Those tops were perfect when I put them in. The only explanation is shrinkage of the floor framing and sheathing. It is rare, but it happens. If the house is built to relatively modern building codes, there is no reason to worry about undersized framing being unable to support cabinets and countertops. If it's been built for several years it's done shrinking.

My house is 115 years old. Last year we remodeled the second floor bathrooms, which involved pulling out exorbitantly thick concrete shower pans. Over the course of a week, I watched the ceiling in my kitchen (which is beneath the bathrooms) lift away from a beam that spans the kitchen. People say old houses have finished settling, but these changes have impacts. (I often think about this when people here are complaining about their waterfall stone issues. I can’t help but think that the weight of all that stones leads to changes in the home’s footprint, even if slight, that prompt some of the problems complained about here that are blamed on stone fabricators).

What is the existing floor framing--joist size, spacing, and span?

I have never had cabinets "settle" Though I have seen land shifts beneath a home, in situations with retaining walls etc.. If you are worried? Get a structural engineer in there before you gut the kitchen : )

Sounds like an early seventies raised ranch to me.......not the best era of construction and lots of shortcuts.