I am working on a story where an alien tells humans that a gamma ray burst will be fired at the alien civilization in one year, as the alien is trillions of light years away, that means that the burst is already on its way and can’t be stopped. The only way to stop it is time travel. Because of this, humans send a time traveler back in time and towards the origin of the message to disable the gamma ray burst before it fires. However, the alien who sent the message knows this will happen and has made a clever and hard to discover set of tests to ascertain when and where the time travelers came from, and uses that information to send the message the time travelers received in the first place. This is because the alien is using paradoxes to find and summon other time travelers to it to make a menagerie. If it can't determine where the time travelers came from it can't send the signal that tells them to arrive. So knowing where the time travelers come from is a requirement for the time travelers to arrive and for the plan to work. However, I’m not sure how to do that.
How can an alien test a time travelled to see when and where they come from? The alien is from another universe, so it doesn’t know about humans or even what galaxy to look in. It also is running this gambit on every civilization in the universe that can respond, so it has to work universally. The alien can make extremely convincing illusions and can even make fake suns if needed, so no matter how hard the test is to implement, it can be done. The tolerance for error is non-negligible, about a 10,000 years and 100 light years.
What tests should the alien use?