Bai shou says Fan yue's intervention in the realm of resentment by saving the child gave Mu jiu a chance to live.…
I think this is just the definition of time manipulation and intervening in the past. Like, Mu Jiu was alive before Fan Yue saved the child because that was what had already happened in the future, it must've happened. I understand it as some kind of a connection between past and future where the past is already affected by something that has not yet happened, but inevitably will happen. This is how I understand this idea.