What happens if someone from the past shows up in the enlightened society of the Federation and we know tha he commited crimes by "todays" standards?
What would happen to a temporaly displaced Djingis Khan.
I will let Flint go because him butchering people as Alexander was such a long time ago.
You just answered your own question. Alexander and Genghis were much alike -- both mighty conquerors who were ruthless to their enemies but benevolent and tolerant to those who accepted their rule, both figures who built the greatest empires of their era and spread civilization widely, and whose successors split their empires into multiple smaller ones. The main difference between them is that Genghis was a lot more successful; his empire was far bigger and lasted far longer. The West glorifies Alexander and demonizes Genghis, but that's simple ethnocentrism; in East Asia, particularly Mongolia, Genghis is revered just as much as Alexander has traditionally been in Europe. ("The Savage Curtain"'s portrayal of Genghis as nothing more than a mute henchman on the "evil" side was probably the most racist thing that ever happened in Star Trek
But what happens if in the characters life the crimes were fairly recent?
Would that temporarily displaced person stand trial?
You'll probably find your answer in this post from the Law and the Multiverse blog:
See also Isaac Asimov's short-short story "A Loint of Paw."