When you are attempting to move out of a red zone where a cleave or AoE is about to hit, whether or not you avoid it is based on where your character is when the cast finishes and not when the animation goes off. The spell finishes about half a second before the zone disappears.

This can be kind of a confusing mechanic for some people because even though they looked like they were well away when the animation went off, they weren't in fact out of the the red zone when the cast finished.

You can actually walk into the red zone at the last second and not get hit. This is helpful mostly for tanks to keep the mob facing in the proper direction to avoid cleaving the party.

The "lag" is an intended feature and has already been adjusted (in beta, you had to move somewhere closer to before 3/4 of the cast) and is a huge improvement now compared to before.

Our own spells work the same actually. When casting a heal, I can move when the bars full even though the animation hasn't even happened and the heal will still land.

TL;DR- Move out of red spaces. Don't wait, don't leave one foot in, don't try to finish your cast, just move.