I checked rule 616 and which states the "affected object's controller [or] affected player" decides the order in which to apply the replacement effects. My interpretation of this is that the spell or permanent who's damage is being increased/tripled is the affected object and that they would chose the order to apply.
Then I was shown the ruling on Torbran which reads:
If another effect modifies how much damage your red source would deal, including preventing some of it, the player being dealt damage or the controller of the permanent being dealt damage chooses an order in which to apply those effects. If all of the damage is prevented, Torbran’s effect no longer applies.
What am I missing in my interpretation of the rules? I've been looking at it for awhile and I just don't understand how they came to this conclusion.