I used to work in the extrusion industry so I’ll take a quick stab at this. All the following is a best guess and absolutely no facts are implied. In the extrusion industry there’s a process called “over-the-core” extrusion, where material (plastic) is fed through a die where the material is formed/shaped around the core (in this case it would be the copper wire). In the case of Romex, it’s probably a two-part process. First, the insulating material (nylon?) is formed over the copper using the “over-the-core” extrusion method. Exiting the extruder the wire goes through a waterbath to cool and cure the material, and is then fed onto a large spool.
Once the individual insulated conductors are on large spools, they are fed into a secondary extruder. The material that makes up the outer jacket has a lower melting temp than the insulating material, so the insulating material maintains its integrity and doesn’t re-melt.
As far as keeping everything “neat and clean” within the jacket, from an extrusion standpoint it’s relatively simple with guides, fixturing, and a properly designed profile die. To give you some idea of capability, we used to manufacture medical tubing with an OD of .0785 inches that was fed over a copper core which was later removed. We were able to control the thickness of each individual wall of the tube to plus or minus .0004 inches.
Hope this isn’t too confusing, and again, no facts are implied………