In order to get Atton to confess his dark past to you, you need to have significant influence with him. You need to take him with you into the Refugee Zone on Nar Shaddaa. While wandering in the "village" there, you will run across two Twi'leks. They say that they know Atton, but not under that name, and that maybe you need to know a little bit more about the people you travel with.
If you have enough influence with Atton, you can ask him about what they meant. He will explain that after the Mandalorian War, he followed Revan and became a Sith. From there, Revan trained him to become a Assassin. He learned to kill Jedi and to keep his thoughts hidden from them:
"I taught myself... techniques. It's hard for Jedi to sense what you're really thinking if you throw up walls of strong emotions and feelings."
It takes a little more influence to find out why he left the Sith:
"Well, there was a woman. A Jedi. She... she gave her life for mine."
The Jedi tried to tell him about the evil Revan was doing, and about the fact that Atton was Force Sensitive. Although he was hurting her, she managed to break his mental defenses and show him the true power of the Force in his mind.
"I think I loved her, but it wasn't that kind of love. It was the kind of love where you're willing to give up everything for someone you don't even know."
"And at the end, I killed her because I loved her. In the end, she sacrificed herself to keep my secret, to prevent the Sith from knowing about that touch of the Force inside me. She wasted her life to save me. Me."
Open and raw with his newly awakened Force Sensitivity, feeling random emotions from all around him and hurting with the pain of the death of the Jedi, Atton fled to Nar Shaddaa, to lose himself in the crowd of war veterans and displaced refugees.
Depending on the Exile's alignment at this point, Atton will ask to become a Jedi for various reasons. For light-siders, he wants to honor the mystery Jedi's memory and seek redemption. For dark-siders, he never wants to be that vulnerable or weak again; he wants the power to kill any who stands in his way.
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