Thanks for this clarification. My understanding is that the Schoenflies theorem states that the two regions of the JCT are, in fact, homeomorphic to the inside and outside of a standard circle in the plane. But does it immediately follow from this statement, that we can then partition the interior of that region into subregions?

Yes, but this leaves something to be desired. What if we had three faces, or more? Would we have to derive a specific version of the JCT for each such case? It seems that something is amiss, there.