I have seen endless debate about this. Here is my experience:
Jump is a Melee attack. Meaning, if I am CLEARLY (I cannot emphasize that enough) standing outside the mob's PBAoE Red Ring of Death, and activate Jump, if my character is still in the Jump animation when the enemy's castbar for it's PBAoE attack ends, my character will take damage.
I have seen several posts to the contrary, most of which citing "lag" as the issue. However, if lag were a factor, that would mean I'd be getting hit all of the time by PBAoE attacks, when I never get hit by PBAoE attacks. I can safely run out of range, use Piercing Talon etc, and be completely safe. I only get hit if I use Jump and am in the middle of the Jump animation when the enemy's PBAoE proc's.