The following if from wiki and the testing done there;
Treasure Hunter - FFXIclopedia, the Final Fantasy XI wiki - Characters, items, jobs, and more
Job Trait Overview
Game Description
Increases chance that treasure will be dropped by enemies.
* If more than one player has the effect in a party or alliance, the strongest version will trump all others.
* This effect will remain active as long as the person with this trait is in the party/alliance, on the hate list of the mob (performed some action on the mob to generate hate), and within experience points range. Some amount of enmity is retained after a player is KO'ed, and also per SE commentary, the treasure hunter effect will remain even after the player has been KO'ed.
* Treasure Hunter is not affected by amount of damage, "luck" items, or who makes the "killshot", nor does it have any effect on chests, coffers, or caskets (including those in battlefields).
* The exact formula for calculating the effects of this trait are still unknown.