Actually, the string example was never meant as anything /but/ a metaphor, and the point is that the three points were arbitrary.

'Past', 'present', and 'future' were just shorthand for 'three different points in time', at least according to what I'd meant. For her, yes, it would have been 'present', 'past', 'farther past'. (That is, 'a' past, present, and future, not 'the' past, present, and future.) The semantics of that aren't as important; it wasn't important /which/ three points, only that there were in fact three, like plotting a point on a three-dimensional space. I don't remember when the game stated that TC had to be done past a certain point--as far as I knew, she needed Ellone becuase she could only reach two points on her own and three JME. To add to this, she needed to be in control of three sets of Sorceress powers in order to accomplish her goal--I've gathered that unless one possesses the link that such powers offer, it's basically impossible to affect the world while placed in the past. (You can't /really/ change the past, but from Ultimecia's perspective, she did, I think, in controlling Edea.) Actually, it might have been the case that it was required that Ultimecia went far enough back that she wasn't born yet, and then far enough back that her 'center' (Rinoa) wasn't born yet, and that was the reason that she had to go that far back--that, and she had to find the only times in which Ellone and JME were active. I wouldn't quote myself on that without more research, but it is one possibility.

The assumption that she casts the spell at three different points does, however, have basis. Why else wouldn't she be able to just do it on her own, in her own time? It's equally possible that she simply needed the vantage point of the different times, or the power boost of using the powers of all three Sorceresses, but it's still a possibility. The exact mechanics of the Time Compression magic are largely in the realm of speculation, in any case.

I don't necessarily see why Time Compression would have to be erased when it was ended under my proposed mechanic, though. It's perfectly reasonable to think that Time Compression would leave its mark on all times, given that they'd all been sort of squished together. In fact, I expect that a few people were actually lost in time, much as Squall and Ultimecia travelled through. It doesn't contradict fate at all, because the string was just a metaphor--and really, I prefer your film image, now that you mention it, for what actually happened.

In short, time can be viewed any number of ways. In this case, there are two that are relevant: outside of Time Compression, time might well be that line, that just keeps on going, with events sprinkled therein--one of which is Time Compression. Time Compression pulls all of time into itself, but it still contained within the grander scheme of Time, because it ended.

On the other hand, there's the view /during/ Time Compression--where it's basically drawing all of Time in on itself. I'd give an image, but I think we have quite enough of them.

I probably should have expected not to get away with being vague when it came to TC, of course. I've read your FAQ before, though, and on the reread it's still interesting. A lot of this can't really be /proven/, but I like to try to find answers that are at least consistent. It helps in writing in FF8, in any case.