In the other timeline where Shinobu destroys the world, Araragi was killed by Tsubasa. Why didn't she help him in that timeline? In both timelines, he didn't find her so what was the difference?
This answer to another question presents a case that Shinobu slipped into Koyomi's shadow about five minutes into Tsubasa Cat Part 4, when Koyomi went to look for her at the Mister Donuts where Mayoi saw her.
If we accept that, everything else falls into place. In the alternate timeline, with no Mayoi, Koyomi has no idea that Shinobu was at that Mister Donuts. He's panicked by her sudden disappearance and overburdened by the return of Black Hanekawa, so he forgets her love of donuts and never even thinks to check the donut shop. Then, as in the main timeline, Black Hanekawa finds him and offers to help look for Shinobu. Black Hanekawa attacks him when he refuses Tsubasa's love, but unlike the main timeline, Shinobu is not in his shadow, and he is killed. Shinobu later finds out and goes on a rampage, turning everyone into zombies.