Before Sam is closing the door at the ending, he looks up! And what is there? For something around 3 sec there is seenable a fire detector! IT IS BROKEN! Someone smashed it, but why ? And who did it?
If the fire detector would be fine ( i mean that someone wouldn't smash it ), then all of the family would be still alive.
Sam jumps back in time to kill his sister.
So obviously, he starts the fire.
To make sure doesn't get out too early, he breaks the fire alarm.
The supposed irony is that in the beginning he saves his sister from the fire, and in the end starts it.
(He could, of course, have just whacked her over the head - but the line about not saving someone being close to killing someone probably had meaning here, at least in the rather convoluted logic of the movie.)
Unless, since part 3 is so different from parts 1 & 2, being more like traditional time travel than jumping back into your own head, the jumping thing is perhaps supposed to change with the daughter, the next generation - maybe she can jump into anyone's body, say her father's, or jump back anywhere in time?
With this kind of movie, you could speculate forever ... <ho hum>