Yeah, this is mostly it, being the complicated, then the extra complicated explanation.
The only thing I would add is the reminder that the analogy for for the worldline is a scroll because human history (and all other history) exist as a continuous 'texture'. If it makes it easier to understand, then rather than it being a tree from which many branches sprout, it is actually a scroll upon which a tree is drawn.
All of what you mention is correct as far as I know, but an additional factor is that since it is "drawn" upon the scroll, what was done was more like a rewriting, than grafting or a reduction to the ROOT. Why is that significant? Because it goes back to what I said about things being on a sliding scale. Some of their perception is not just coming back from a recognition of a logical scenario in which Illya used to exist, but also from the original 'texture' which was present that had been overwritten.
I would actually argue that both analogies are somewhat incomplete. As the ROOT and description of it implies, all of existence in nasu's timelines work more like a program and recorded data. The ROOT therefore has the same meaning as the root in computer science, and is where the 'source code' lies. As one timeline is overwritten or modified, this is akin to the same operation on a data storage device. But just like the ones in real life, data is never truly destroyed unless it is completely overwritten, and sometimes it has to be overwritten multiple times else it will still exist. Well, that or degaussing the storage would do it.
Imaginary number space therefore also fits into this analogy as something akin to quantum mechanical memory. It is not directly observable and consists of all possibilities, as it's state is determined by probability rather than absolute values, and is inimical to "real numbers" space. Actually, more specifically it is likely that both real and imaginary number space is something like collectively the memory of a quantum computer, with the imaginary "reverse side" being all the possibilities that the real side isn't, and consequently also 'nothing', from a quantum computer's perspective. As a result, imaginary number space is likely the medium through which this 'bleeding' effect between different versions of the world passes through. Actual data can be stored in it as well, like in the case of the Pithos.
As an aside, Mooncell of Extra-verses works exactly like this, which is why it's capable of acting as a physical mirror of the worldline framework.
