Francisco and some readings and close observation of a caprifig firsthand last year are my teachers, but I don't claim to be an expert. But here is what I know. At this time of year, the caprifigs (here) are without leaves and they can be spotted in the wild easily as their branches have plump figs on them. These are the mamme crop. These figs have wasp eggs on them which often can be spotted as off-white galls inside the fig if you cut open the fig. Right now, in my climate, the profichi crop is also forming, seems to be about the same time as breba on some of my common figs. The mamme crops function is simply to serve as a place to hold the wasp population until the profichi are ready. The profichi are the most important crop of caprifigs. In maybe another month from now (in my area) wasps will emerge from the mamme and eggs will get laid into the profichi. Again, in my climate, wasps will emerge from the profichi in early July (late June near Fresno, I believe). The profichi have pollen and the wasps leaving these figs will venture out to other trees and perform caprification. The next step remains a mystery which Francisco said people don't know what happens. On my closest caprifig which I successfully used to caprify Marabout c. Smyrna (very successfuly with just a couple of fruits about 2 or 3 times, a week or two apart), I see no mammoni (the third crop) on the branches when the profichi drop around August or so. I do not know where the wasp population resides for the next couple of months. I don't recall specifically when (chestnut season keeps me very busy, remember), but maybe around October the mammoni crop forms and these simply serve to hold the wasp population over until the mamme are ready.
One might be able to get profichi with wasps in them from other areas but I think the timing will often not be correct so I think it's best if folks try to grow their own if they can keep them from getting too cold.
The fig wasp is not considered a pest and USDA does not regulate movement of the insect. One official in another state had told me to obtain a permit from APHIS before shipping wasps to her state back east. When I told her that APHIS officials told me that the wasp was not regulated, she dug around for a while and saw that the caprifigs could harbor fusarium wilt and that California has a regulation that requires that the mamme be picked up from the ground to reduce the presence of this pathogen so that they are not spread to commercial fig crops which can lead to spoilage. So she said that she wanted a phyto on any profichi shipped to her state to help protect her state's non-existent commercial fig crop. This was not be feasible as the profichi would be dried up and the wasps gone before my local ag officials could send off the profichi to a lab to be tested. As it is, fusarium wilt is already abundantly present in our environments. Nobody picks up any mamme figs from the wild trees around here, including my neighbor's tree that I used. I experienced no spoilage other than over-ripe figs becoming sour (I can't always keep up, no matter how hard I try!).
Once a wasp enters an edible fig it is believed to never leave and is absorbed into the developing pulp. Compost fertilizer, of sorts. Their wings reportedly often fall off when they squeeze into the eye of the fig.
Another mystery to me is that once my Marabout c. Smyrnia were caprified in July I continued to harvest ripe fruit from maybe late July or early August into late October. I don't think that the fruits that I picked in October would have been developed enough at the time I placed profichi amongst the tree so I don't understand how they were caprified. Maybe they were, in fact, receptive in July and just take longer to develop and ripen because of their location on the branches.
Vista split on my least year for the first time that I remember and I think it was probably because it is more sensitive to excessive pollination. Maybe 25% of the fruit split on me.