Schwarzschild black hole spacetime in Kruskal-Szekeres coordinates

First, a brief introduction to provide the right context. I've been studying General Relativity with Ohanian and Ruffini's Gravitation and Spacetime. They introduce Kruskal-Szekeres coordinates for Schwartzschild spacetimes in Section 8.3 (Maximal Schwarzschild geometry) and show a spacetime diagram in such coordinate system:

In particular, they say "This second space is in a different universe; alternatively, it may be regarded as a region in our own universe, if this second region of our universe is very far away from the first." and "However, if astronauts from both universes jump into the black hole (region II), then they can meet, embrace, and perish together." I'm not sure I got it right but I infer two possibilities:

• the same black hole exist in both universes; or
• the same black hole exists in two different regions of the same universe.

Is this correct? If so, what are the implications? Should we expect an unidentified grow of the black hole's size as there would be invisible matter (from our point of view) from the other universe (or region of our own) falling into the black hole?