> But wouldn't these causally disjoint regions overlap with each other

Yes.

> stringing together a chain of causality from anywhere to anywhere?

No? Causality reaching one edge of a sphere doesn't mean it instantaneously teleports to every point in that same sphere. This isn't a transitive relationship.

> What are "disconnected events"?

The sentence you're responding to seems like a decent definition. Disconnected events are events which might be observed in either order depending on the position of an observer.