There are probably several different chemical compositions used for caulk, but my understanding is that they generally set on contact with air or at least the moisture content of air. There could also I suppose be an element of evaporation of a solvent involved.
So how does the middle of any given bead of caulk set? Caulk is pretty much water and air proof.
Another thing I notice is that it an unopened tube has a shelf life measured in years. However, once you open the tube, it slowly sets starting at the tip of the dispenser but, left long enough, it eventually it sets right down inside the tube. Yet once the caulk in the very tip of the dispenser has set, there’s no way for air or water or evaporating solvent to get in or out of the rest of the tube.
The only thing I can think of is that it is set off by a process that permeates through the unset caulk. I suppose that has to be it by a process of elimination, but it still seems surprising that it can set well into a tube of caulk due to a hole in the tip of the dispensing tube, despite some inches of set caulk in between.