This particular quest bug is a known issue, and the team is currently working on a solution.
In the meantime, there are a couple of things you may try to resolve this issue:
Type /reloadui in the command line of the Chat Box
Try performing a soft reset: log out of the game and launcher completely for at least 15 minutes. This will reset your character's instance information and may cause quest NPCs to work properly.
Abandon and restart the quest, which also causes quest NPCs and objectives to restart; this generally gets positive results.
Should you require further information, please reply to this e-mail.