Below is a photo of a recent quartz countertop install where the the backsplash does not sit flush with the sheet-rock wall. This can happen from time to time and is considered an "unforeseen". Unforeseen occurrences are generally not included in a project estimate.
A quartz or granite backsplash will always be cut straight. Unfortunately, sheet-rock walls are not always straight.
The solution? Depending on how bad the gap is...
Sometimes paint-able caulking can disguise the problem...
Another option is to cut the backsplash (add a seam to the backsplash) in he middle of the gap.
A third option is to build up joint compound where the wall does not meet the back of the backsplash.
For large gaps... Backer rod may be necessary to fill in the void. Backer rod comes in many sizes and is available at your local home improvement center.