It is your second option... probably
The phrase about damage supplements previous one about determining bite's attack bonus during full attack. So it talks about your Strenght bonus to that bite attack under certain circumstance only - you make a full attack combining manufactured and natural weapons. For that specific situation, rules say
Creatures with natural attacks and attacks made with weapons can use both as part of a full attack action (...). Such creatures attack with their weapons normally but treat all of their available natural attacks as secondary attacks during that attack, regardless of the attack’s original type.
The only thing Animal Fury really does, it gives you a bite attack while you rage. When he isn't making full attack your character uses the folloving rule
Primary attacks are made using the creature’s full base attack bonus and add the creature’s full Strength bonus on damage rolls[...] If a creature has only one natural attack, it is always made using the creature’s full base attack bonus and adds 1-1/2 times the creature’s Strength bonus on damage rolls. This increase does not apply if the creature has multiple attacks but only takes one.
This is actually a really tricky point which of the above sentanses (bolded or not) should apply to a charactr able to perform attacks with manufactured weapons, but who has only a single natural attack. Pathfinder bestiary isn't realy helpful here because of a way creature's statistics are given. But Pathfinder is a direct inheritor of dnd-3.5e, where statblocks were a bit different and can provide some help here. Here are Minotaur and Bralani entries, which both indicate 1x Strength modifier on a creature's single natural attack used not as part of a full attack. I searched more, and was unable to find any monster, who use manufactured weapons and gains 1.5 Strength on a natural attack. Your cannibal example also match this.