Suppose, maybe, that the Time Matrix was somehow some weird side effect of the (equally weird) process of Ellimist/Crayak's creation? They go through the black hole into the other side of reality, and at the same time this random little white sphere pops back out, on our side? One of those 'conservation of matter/energy' things. 'Conservation of reality,' maybe, might be a better term, since conservation of matter/energy don't really apply to the Ellimist or Crayak.
Anyway, I see it as sort of an anchor or something. A thing cannot exist, with no connection to reality at all, right? So, maybe, the Time Matrix is simply that root, that holds Crayak and the Ellimist to this universe. Or, perhaps, another apt comparison might be the morphed matter that goes into z-space when someone morphs a smaller creature. It's just something that's there, because it needs to be.
It can time-travel and create new realities, quite simply, because the Ellimist and Crayak can. It's of the same reality-non-reality as they are, but it doesn't have sentience of its own (why should it, when it's just a random blob of wibbly-wobbly-timey-wimey stuff sorry couldn't resist), which opens it up for anybody to take control of it. And it can't be destroyed, so, basically, the Ellimist and Crayak are just stuck with this stupid little thing that neither of them wants to exist but does anyway.
It all still fits with canon, of course, because technically they would still have 'created' it, by virtue of their own existence.
But this opens up a startling possibility. Since the Ellimist and Crayak each came into their own plane of existence separately . . . it is then entirely possible, according to my theory, that there are two Time Matrices out there. Can't really prove otherwise, can you? Certainly an intriguing thought, that there could be another one out there somewhere.