Kurt was picked up by some government agency (like futuristic weird government agency) to be able to go back into his timeline at various points and change events and see how that correlates to their life. I can't remember if the agency was doing it for experimentation or it was already well founded, but they pull him into the future for these tests. They find that he has a lot of variations in his timeline, and that he's actually pretty good at figuring things out despite jumping into different age ranges of his body. While he's off of his "missions," there's a woman there with him guiding him through the missions and feels bad that they picked up this teenager and he's not allowed to go back to his family.
There's a sequel to this fic as well, where Kurt manages to get out, but they want him back to run more simulations/missions.
I think there is reference to the butterfly effect. That's all I can remember about this story, and I would seriously love to find it again!!!