Actually it sort of depends on what you mean by dimensions…but what you say is, I suspect, getting towards the truth.
It turns out that the alternate realities are all caused by using different dimensional sets.
There are in fact an infinite number of possible dimensions, humans/demons can only perceive/occupy/exist on so many dimensions at one time. Which combination of dimensions you occupy determines what reality you are experiencing.
Traveling between planes is basically changing which set of dimensions you are occupying at any given time. This is string theory/quantum topology.
My suspicion is that you are correct and there is some very “special” dimension of space time that the abyss occupies (along with some others) and demons somehow always occupy this dimension as well, even when they on various planes.
When they are killed it’s this “extra dimensionality” that they share with the Abyss that allows them to regenerate in the abyss.