Logic tells me that forensics would have discovered her dead near an UNLOCKED door. They would have investigated to figure out why she didn't leave out of the door. They would have known he "murdered" her. So realistically when he jumped back to present day he would have found himself in a jail cell.
I see why you would think that however, to be fair to the movie, we see the house begin to collapse so there would be no guarantee of where his sister would have ended up positioned. Also, even if the house had not collapsed, it is very common for people to become so disorientated - both visibly by the smoke and also carbon monoxide starving the brain of oxygen - that they can be right next to an exit without realising it before they are overcome and pass out. As such, even if she did end up positioned next to an unlocked door it would probably not raise any suspicion at all.
Police suspicions would probably only be raised if it was discovered that the fire had been started deliberately and that it was likely one of the family that had done so. Both of which we can assume were not the case here. In a real-life case I don't think there would be any suspicion of any foul play at all, especially if the actual cause of the fire was found to be accidental. I would imagine that in the case of somebody being murdered and fire being the cause of death, the fire itself is likely going to be deliberate in the first place.
it begs to question though how did she die in the original setting?
it seems like he didn't really need to save her, because in this situation he prevented her from getting out... whereas before he actually had to save her to make her live...
so why couldn't have just NOT save her rather than intentionally trapping her?
That was the only logical thing I didn't get...why he needed to hold the door? If they found her by the door, they probably would have just figured she passed out there, not that he "murdered" her...people die in fires all the time, it's not like everyone always gets out. BUT if she died the first time, then it seems that the only change he would have had to make was NOT saving her...and she would have died on her own, right? Because that's what happened the first time when their parents survived. If she died anyway, he wouldn't have needed to trap her. "You should have a degree in being wrong...all the time!" ~ Shawn Spencer
Logic tells me he couldn't have held that door shut anyway since the metal would've been hot as effing hell. I mean seriously, they teach this to little kids. In a fire, the door knob is hot if the fire is in the room.
Also: the odds of somehow the two being a foot away and somehow the fire eats her up to the point that she can't open the door before he walks away UNSCATHED.
Well he killed her in the first place.... So came back and saved her... And then killed her again... The problem is why he wouldn't remember it if he had jumped in the first place...