This Movie did not go by reality
When he first jumped to change the murder. Why would he even have the same obession for the murders that he did from the age he went back before the murders, til he apeared in his apartment.
shareI'm not sure I understand the question, but at the beginning of the movie, Sam was obsessed with his girlfriend's murder 10 years ago.
Then, whenever he would meet a new girlfriend and fall in love, his sister would go back and kill her before they met, so that he would never meet the girl.
Only the police would know that there are similarities between the victims of the sister, since she remembered timelines that Sam did not. When Sam, playing "police psychic," came into the station, the cops showed him files similar to his girlfriend's murder.
As his sister kept going back in time and killing more people, more murder cases would appear in Sam's file, even though those people were not murdered in previous timelines that Sam remembered.
Every time he got back to the present, someone else would be dead in the new timeline, so he thought something he did caused the new murders (which would be the logical assumption if he were the only time traveler in the Universe).