This question is puzzling us from the beginning of time travels in Lost and a theory comes from Jeff Jensen of Entertainment Weekly on a “Totally Lost” episode;
Dan Snierson: I guess the big question now become, I’m trying to, you know, unpack all the rules of time travel, so does this mean that when Danielle shows up in season one and meet Jin, does she know that she had an encounter with him?
Jeff Jensen: I say that, she did recall Jin because my theory on the time travel on the show is these memories aren’t uploaded or booted in peoples’ heads until both parties have the experience.
And he gives the Daniel Faraday and Desmond Hume connection we saw last year; Desmond visited Faraday at Cambridge in the past but Faraday came to the island with no memory of this meet up. Desmond’s visit to Faraday was a trigger and once Desmond has that experience both of them have the memory.
Sounds good enough for me. You can watch the video below: