If you examine what a universe would look like "from the outside", so to speak, it would look like a black hole. Because the new universe looks like a black hole from the outside, it is unable to expand into the pre-existing universe. But it has no trouble expanding from the perspective of somebody within the new universe.
That is, if a new universe was generated from a vacuum fluctuation in an existing universe, it would look like a microscopic black hole that came into existence for a moment, then rapidly evaporated away. One way of looking at it is that the space-time of the new universe "pinches off" from the old one, and almost instantly the new universe is all on its own, with no connection to where it came from.