An opening measured at the back is not the opening measured at the front, and neither matches what it is 100mm off the floor. In a house with lath and plaster behind the drywall, the spread between the largest and smallest of those figures is routinely 10 to 20mm. A cabinet made to the largest will not go in; one made to the smallest goes in surrounded by gaps. So it is built a few millimetres undersize with scribe stiles standing proud at the ends, and the fit is cut on site against the wall that exists.
Level comes before plumb, and the floor is what loses. The carcass is levelled to itself and packed clear of the floor, and the plinth is then scribed down to whatever the floor is doing. Doing it the other way round — standing the box on the floor and correcting at the top — puts the error into the one horizontal line visible from the doorway. Where a wall leans outward the gap shows at the rear edge of the counter rather than at the cabinet, so scribe allowance is planned for the top as well.
Fixings go through a back rail thick enough to take them, into located studs or blocking, with a packer behind every fixing point. Without packers, tightening a screw pulls the carcass into the hollow of the wall and racks it, and the first thing to show is a drawer front no longer parallel with the one below.
Then the connections. Existing stops frequently sit at a height that lands in the path of a drawer box, and old chrome-plated valves untouched for twenty years often will not close, so replacing them is scope rather than a surprise. Finally the junction with tile: whether tile runs behind the unit or stops against it decides whether the cabinet can ever be changed without retiling, and the joint itself is sealed flexibly, never grouted, because the two surfaces move independently.