From Dark and Darker Wiki
The treasure hoard page says it rolls only once for the chest per interaction. The x3 per pile is only for standard treasure, like gems and trinkets.
It rolls 3x for treasures (gems, trinkets, etc.) It rolls 1x for gear loot It rolls 1x for gold/silver coins in amounts that can go higher than 1 stack and finally rolls 1x for the chest
So each interact rolls 6x, but only one of those is for the chest specifically