Most figs don't cross pollinate. Desert King isn't a common fig but it still doesn't need pollination to set the early breba figs. It does need pollination to set main crop.

In Z7 you aren't going to have fig wasp and you don't have the caprifigs that provide pollen. The pollen producers are not common figs rather caprifigs.

Pollination has nothing to do with how your fruits are looking. You'll know at some point if what you have is really DK.