Ran another mission, counted up the successful attacks and heals again:
Cross Punch : 38 attacks, 1 heal, 3%
Shadow Blast : 38 attacks, 1 heal, 3%
Kick : 51 attacks, 3 heals, 6%
Gravity Well : 27 attacks 0 heals
Sunless Mire : 9 attacks, 1 heal, 11%
Essence Transfer is in Gravity Well, which happens to be the attack that hasn't fired the heal. Not counting Gravity Well, there's a 4% chance to fire the heal across the rest of the attacks, same with my previous run -- well below the stated 12%.
Also: Essence Transfer heals around 24 against same-level enemies at level 23. This is similar to what the Corruptor's heal pbaoe proc heals for. Since this isn't pbaoe, I'd expect it to heal for more, or more often.