Q. I saw a treasure chest while I was out doing a regional levequest! Is there always a treasure chest somewhere on a levequest!?
A. While on a regional levequest, treasure chests may appear based on the levequest location, but there is no guarantee. The chances of a treasure chest appearing, however, may be increased through leve linking.* Upon opening these chests,** players will be rewarded with gil and, in rare instances, items. Should a chest be opened by a player in a party, gil will be automatically split and distributed to party members on the levequest, while items will be placed in a random member’s loot list.
taken from Lodestone page here

Directly from Lodestone....




The only thing is those chest are not the ones that drop after killing the NM on your T3 Faction Leves. Those are just random chest on regular Guild Leves.