It's not when they do something different, it's when there actions cause a change to the events that the big bad is needing. Because whoever the big bad is, they have an overall outcome that they want to achieve. E.g, classic loki lived the same life as our loki, but when he attacked thanos he actually used a illusion rather than doing it himself, and then hid in some debris and floated into space.

As far as thanos and the avengers and everyone is concerned, classic loki died at that point as the illusion was so strong. And then when classic loki lived in isolation on a planet for thousands of years, it made absolutely no impact to the desired timeline that the big bad wanted.

It was only when he tried to leave the planet to go see thor that it then caused a branch, because at that point the effect of the believed to be dead loki suddenly appearing would change people's actions and the events that follow and ultimately cause a branch to the outcome that the big bad needs.

Timelines can be very different in each multiverse as long as the overall outcome is the same.

E.g in every multiverse the infinity stones would have been collected by thanos and he would have done the snap, as that is clear an integral part to the sacred timeline. How he got the stones may have been quite different from universe to universe