No new space is created (outside of the wormhole) by the wormhole.
The curvature depicted in the image is just to portray the idea that a traveler going from one side of the wormhole to the other will take a longer path. That is, that we can understand the wormhole as a shortcut.
The background of the image is unfortunate, you should disregard it.
The wormhole is about the topology (read: connectivity) of the universe. If you can have an otherwise mostly "flat" universe where two distant points are connected, so that you can travel from one to the other, you have a wormhole.
Now, how do we show that to kids?
Well, we can have a sheet of paper that represents the space-time, curve in such way that it touches itself and go "look, if you create a shortcut you can travel the vast distances of space in an instant".
but the wormhole is not about curving the whole universe to make two points meet. Well, maybe it is, we can't create these things, you know? - It is about two distant points connected, just because it is possible the universe have those (the equations of general relativity can be solved for a topology like that).
It is probably better to represent the wormhole like this (except now it doesn't look like a shorter path):
People not to scale
Besides the representation of the curvature as a surface is misleading...
It is better to visualize it as space becoming "denser":
At its core, this is intended to show that distances nearby the object (earth in the pictures) are shorter. But we don't have a good way to show wormholes in this representation.
Addendum: In case it wasn't clear, I'm saying that the "created space" is an artifact of the representation, and there is no new space created at all.