This quest is very broken for Demonology 'locks right at the moment.
See post here: http://us.battle.net/wow/en/forum/topic/6520712066?page=1#2
Confirmed myself that switching out of Demo spec worked. The minute I re-accepted the quest from Aggra as Affliction, the script started and progressed as intended, whereas while Demo, the script never started and getting to 100% of kills did nothing.
If after you drop the quest, you have to leave to train a new spec, you're on your own to get back.
You can easily fly to the island above SilverTide Hollow from the farthest West point of Dun Morough via flying mount if you've never opened up Vash'jir (I hadn't.) With the new B.net mount sharing, I had the Abyssal Seahorse from another alt, so I simply mounted it, put on water breathing, and swam the rest of the way to the Abyssal Maw where I talked to Aggra in order pick up the quest once more.
Very much a PITA for a workaround, but at least you won't be stuck. :) Good Luck!
Edit: the next quest in the chain, Elemental Bonds: Patience, was also broken as Demo. Just stay Aff or Destro for the rest of the chain and save yourself some grief.