Fires when the player is looking at the "Complete" page for a quest, at a questgiver.. This is the portion of a questgiver dialog in which the player is offered to choose a reward (or accept the only reward) and sees the "Complete" button available. This event does NOT fire when they actually complete the quest, it fires when they SEE the "Complete" button and are offered the ability to complete the quest, and has nothing to do with whether they actually turned in the quest or not.
To avoid confusion: This event should not be used if you want to know when the player actually turns in a quest, that's not what this event does (see above).
This event happens after the portion in which the questgiver verifies the player's progress on the quest.