Yeah, i re-watched the first episode cuz i was curious about Kurisu being dead, it would appear that in the first timeline Titor met Kurisu and that led to her death, perhaps Titor wasn't the only one who passed into the past, it could very well be Okabe as well, and when he saw Kurisu he wanted to warn her about something, that is why she followed him, and how sh survived what ever was supposed to happen to her.
That Said, how can we be sure Titor is a good person ? if okabe leaped after him it was for a reason, or it's vice versa ? What ever happened, Titor was sent to 2010 instead of 2000, there can be some connection to Titor knowing Kurisu earlier in the first timeline, and maybe Okabe decided to save her, and why he was there talking to Kurisu, or it just could be something entirely different...