Man do I love time travel stories. I'm curious to see how you adapt the game to fit the "whether it comes to pass or not" part. Do the things that happen to your object reinforce the time loopiness/the idea that the past and future are concrete so that you have to work toward some kind of preset condition? Or does every change imply a "you crush the butterfly and everything is changeable" time travel rule?
It's more a case of, at the end of the game, you figure out two things: what future you came from judging by how people reacted to you, and whether that future came to pass because of how people acted using you. For instance, if everyone who used you suddenly began watching the skies and reading up on aliens, you can guess it was an alien invasion. And if no-one using you bought you to wider attention or used their power to try and change the course of history, aliens probably happen again.