Since there's no concept of space and time "inside" a blackhole, I think it would be better to think of blackholes as doors to different rooms in a huge mansion rather than each room having a smaller room contained inside it.
Space and time still are well defined inside of a black hole. They only break down at one point, termed the singularity. But nothing mystical happens and neither space nor time break down when you pass the event horizon. So there is indeed a well-formed notion of "inside", as long as you're not in the very center, where the singularity breaks everything.
A black hole is technically a single point. The part of the hole that we colloquially refer to is the event horizon. The headline speaks of universes "inside" a black hole, not an event horizon.
There's a brilliant explanation on reddit by RobotRollCall on this topic. I'll update my post when I find the link.
