It's been many years since I was invited with particle physics, so it's a bit muddled in my memory... i could be wrong on the details here. It could be the CP symmetry instead of the CPT symmetry.

It's not that positrons go back in time, but more like "if an electron went backwards in time, it would look exactly like a position". The Feynman diagram of an electron and position annihilaton is the same as that of an electron bouncing on photons, expect the angle is rotated such that the electron bounces backwards in time.

https://commons.m.wikimedia.org/wiki/File:Feynman_EP_Annihilation.svg#mw-jump-to-license