One of the more common theories regarding the medieval "conveyor belt" approach is as follows:
Staves would be selected (not sure by whom) and worked down using a series of facets to the standardised shape and tapers. These would be virtually pre-tillered, as if you take for example the MR dimensions and apply them exactly to a stave, the bow is ready for bracing almost immediately, and needs just a few tweaks to perfect. With a bit of bravery you can take a well got-up yew stave and turn it into a shooting warbow within an hour. The more experience, the quicker the process.
The bowyer himself would then refine the tiller using a flote or similar tool (as can be seen in the tool marks of the MR bows) and the tillering would be complete.
The horner would have access to the very tips of the cattle horns, which (if taken from the animal at the right time) would already have the perfect hollow naturally inside them, and would require very little drilling. They would also require very little shaping if the absolute tips are used. The hollow horn tips would most likely be sent to the bowyer in box-loads. The bow tips would be piked to fit the hollow (giving that lovely natural rounded shape seen on all the MR bows, as compared to the straight-edged taper seen more often today) and glued into place.
The stringfellow would be responsible for making the strings, and these would be stored separately if we're using the Tower Of London's records as a guide on this.
I think it's a very modern idea to have a "perfect" tiller, as everybody stares at photos of bow tillers using arcs, circles, flipping tools and so on but when you're making bows in the countless thousands, this is just impractical. A roughly tapered and tweaked bow stave will come round to about 30" or so with very, very little work and when you're not expecting them to last for many hundreds of shots a stiff limb here or there wouldn't be worth worrying about, where-as today we'll spend hours and hours refining a tiller to make sure it's "perfect" because each bow is special to us. Remember that the medieval bow was a tool, and the MR bows aren't sanded or finished in any way, with no grips and often not even a bowyer's mark.