This looks to be fixed??? I was able to complete it and saw someone who had no loot able to complete it too!
I just abandoned the quest, re-aquired the quest and then it worked 3/3
Went away and did other things for awhile, came back and they are lootable. Hopefully that means it was hotfixed and working for everyone.
First time for me as well and it’s bugged.
I can confirm that this morning, I picked up the quest again and was able to open all three chests successfully and complete the quest.
I have all the quest items checkboxed as done but cannot turn in the quest. Tried leaving the island and returning, which sometimes fixes the turn-in problem, nothing. Can’t turn in and complete.
Edit: went back to the cave where one of the chests is, ‘found’ it again, went to open it and it vanished and got the ‘objective complete’ message.