What Mr. Laser Beam said; it's not a branched timeline, it's a completely separate reality.
That's a spurious distinction. Of course it's a branched timeline -- just a spontaneously occurring one like those seen in "Parallels" or
Myriad Universes rather than one created by time travel. It has the same stars and planets, the same species and individuals, and many of the same past events, just happening a little differently. That's the very essence of a branched timeline. If it were an entirely separate universe, it would have entirely different stars, planets, and species, even different laws of physics.
Sure, if you invoke the "infinite universes" excuse, you can claim that any random combination of particles is bound to occur somewhere just by chance, so that there would be near-duplicate realities that weren't related by being branching timelines; but as I've pointed out before, the counterargument there is that if there were an infinite number of possibilities, the odds of reaching a given one would be infinitesimal. The fact that the Prime and Mirror Universes interact so frequently, on top of the persistent parallelisms between them despite their differences, just drives home that it has to be a closely associated quantum variation of the same physical universe, i.e. an alternate timeline.
I'm always bewildered by the assumption that a time travel-created branching is somehow a fundamentally different thing from a spontaneous branching. That's like saying that a lake created by a human-built dam is somehow fundamentally different from a lake created by a naturally occurring rockslide or something. Or that a piece of ice that comes from your freezer is a totally different substance from a piece of ice chipped off a glacier. The physics and properties are the same regardless of the difference in the causes.
But yeah, it probably falls out of their jurisdiction, because it's not particularly about time travel. It's an alternate timeline, but its present and the DTI's present are concurrent. Parallel lines, instead of trying to hop points on the timeline.
Actually, I've shown in both my DTI novels that parallel timelines do fall under the DTI's jurisdiction. They handle anything involving time -- not just time travel, but parallel timelines, counseling time-displaced people (even those awoken from cryogenic stasis), you name it. Not everything they do has the same existential stakes as guarding against the rewriting of history.
After all, it's the Department of Temporal Investigations, not just Enforcement. That means learning all they can about any time-related matters, both to assess any potential threat and simply to gain further understanding of how time works and how to manage its risks. Alternate timelines are a part of that.