I've never hunted with double triggers or known the correct way, but it seems most SxS doubles I've seen have the more open choked barrel being fired by the front trigger and the tighter choked barrel by the rear trigger - which all makes sense to me.
The triggers have also been staggered with the forward one sitting to the right of the rear trigger. This has always seemed bass-ackwards in my little pea brain! For a right handed shooter, it always seemed to me that the front trigger should be staggered to the left side. After firing the first barrel, your finger could then just slide back to the second trigger.
I'm with the OP... I'd be curious to know the correct way of operating them!