You don't really NEED to move until the twister bar is about 1/2 to 2/3rds completed with its cast. It's like any other ability...the skill does not actually happen until the cast bar is complete...so you don't have to stress if you didn't start immediately after the cast bar has appeared. Just don't retrace your steps and you're good.

Our group ran in a "U" or "J" path. This seems to be the best way to move if you want to avoid crossing someone's path as it minimizes the actual side-to-side area you take up. Additionally, when twister is cast, we had EVERYONE that sees it call out the cast on voice to ensure that everyone knows it's coming.

This phase and the twister mechanic itself are much easier than any of the phases before it. Just don't overthink it, and you'll be fine