Re: finding treasure in the cave in Sulani
No, I don't think you're doing anything wrong, and I doubt it's a bug. When you explore the cave, what you get is random. Sometimes you find something, other times not. And when you do find something, it's nothing you can't find other ways like fishing, diving at the buoy or beachcombing. So, the things you can get can be a crystal, metal, fish, mermaidic kelp, one of the 18 Sulani collectible treasures or a few simoleons. You're not looking for something different or special that you haven't seen before if you've played Island Living for a while.
Now, I haven't ever done that odd job, so I'm not sure what the exact wording of the task is. If you are finding things and it is not registering as found for the task, then that could be a bug. Or else, the task requires finding a very specific thing or requires you use a specific cave option. There are 4 options to explore the cave and only one might count towards the goal. If you haven't already tried using all the options, you should try them.
So, are you not finding anything when you explore the cave or are you finding things and the task is not completing? From the way you worded your post, I think what you might be looking for is one of the 18 Sulani treasures. Tbh, I've found those are hard to get from the cave when I'm working on the aspiration.
Hope this helps.