The problems Sam encounters when he attempts to discover Rebecca's killer arise because the killer is also a time traveler, and one with intimate knowledge of Sam's intentions: his sister Jenna. This also complicates our analysis, because we do not know when Jenna makes her trips, or what trips she has made.
We can, though, conclude that she was very young when she made the first one. She is a few years younger than Sam, and most probably made a short trip to the past to kill Rebecca. To reach that conclusion you have to understand Jenna, though, and that involves the fire.
In the original history, Jenna died in the fire, but Sam and his parents escaped the burning house. Sam cannot live with that outcome, so sometime shortly after the funeral he travels to the date of the fire, gets a ladder ready, and when the house is burning he climbs to the second floor window and rescues his sister, carrying her down the ladder. He having saved her life, she is completely devoted to him.
We could say that no girl was good enough for Sam except Jenna, in Jenna's opinion; and she wanted her brother to be solely hers. But what mattered with Rebecca wasn't that she was taking Sam away from her, but that she was cheating on him. Eventually Rebecca must have told Sam, breaking his perhaps eighteen year old heart (Elizabeth is the younger sister, and is driving at the time of the murder, but they are all in high school). Jenna kills Rebecca before this revelation, but would not have done so too long after the fact--people recover from high school breakups, and it is evident that Sam and Rebecca did not stay together (when Sam has undone all the deaths, he is married not to Rebecca, who is present at the party, but to Elizabeth). The infidelitous Rebecca must die, in Jenna's view, for the hurt she caused her beautiful Sam. So she makes a brief hop to the past, kills Rebecca in her own bed, setting it up for a time when she knew Lonnie was coming over and then framing him for the murder.
This is exactly the sort of paradox that makes the Butterfly Effect franchise so difficult, as the rules keep shifting and the viewer is never told how. Both the fire and the murder give us anomalies that result in impossibilities, effectively grandfather paradoxes on a smaller scale, in which what the time traveler does prevents what the time traveler does. We will begin looking at that problem next time.