The disturbance detected quests are required to be picked up BEFORE the boss is first killed each event lockout. If you pick up the quest after, then kill the boss again, the second boss kill does not drop the quest item needed to complete the quest for that time walking event. This results in the player being unable to complete the quest entirely for the remainder of the time walking event.
When you run a time walking dungeon, the first dungeon of the event, the final boss drops an item that starts a quest you are able to hand in for reward. There is no pre-dungeon quest needed; simply kill the boss, loot the item which starts the quest, and hand in.
Why is the raid different than the dungeon? The user experience is that the player is denied the quest for the remainder of the time walking event.
Suggested experience: The raid boss always drops a quest starting item to hand in for reward. Alternatively, the quest does not require an item to be looted. Alternatively still, the loot lockout does not prevent the item from dropping.