They do use a jig, actually, it's not freehand carving!
The one they used on me is like a router circle jig, and the thing is clamped over the eyball and a scalpel-like blade rotates at a set radius (typically 8.0mm diameter or so).
My first was an 8.0mm patch sewn into an 8.0mm hole. The second one (the one that is now failing) was an 8.0mm patch sewn into an 8.2mm hole, stretching it a bit flatter so that it focuses a bit furthe back, closer to where it should be (on the retina), so that less correction is required. The trouble is that even the new cornea is all wrinkled and knackered, so without a smooth contact lens to clad it, the vision is stil about 6/360.
That Israeli jobbie above comes as its own kit, by the look of it.