I have been following this story very closely, looking for little clues. Now you said:

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if you want to figure this thing out, pay attention to what isn't in this story as much as you pay attention to what is in this story.
There was no "Tempus Fugitive." Am I on the right track?

I'm even going to go out on a limb and say that they didn't mess up their past. Somebody (Tempus) else did, or they are not where they think they are.

Keep 'em coming. I love a good mystery.