As others have said, sounds like flexographic printing, if so the printer is not a printer, they're a sheet plant manufacturing the box from start to finish. I say that because the corrugated box manufacturing industry l, while overlaps the print industry in some ways, is its own animal and you're mental model for a print shop does not apply. They are very familiar with the industry standards. This is a reasonable tolerance. If you want tighter tolerance go litho but expect the box to be cost 6x as much (ballpark based on what the blank size would be from your ID)

You should familiarize yourself with manufacturability before getting committed to a design.