Un amico bisognoso
Sembra che un altro potenziale sopravvissuto, James Oxen, abbia lasciato una lista di provviste. Sul retro c'è uno scarabocchio di una caverna. Raccogli le provviste, trova la caverna e proteggi i sopravvissuti.
Lista abbandonata 
It worked for me after abandoning the quest and doing everything again.
Kill 3 Angry Earth outside the cave, if it doesnt give you completition, make a camp outside to the left of the cave and stay in the unnamed area until the 3 Angry earth respawn again, they should respawn with a marker on top, kill them, complete quest with the NPC in the cave.
Cave location Elysian Wilds South West (Dance of the fireflies)
Guys, if the entrance to the cave does not count, then I did this - I went into the cave, switched to the character, left the cave for a short distance and went there again - it worked.
No quest maker appears for this quest, no idea which cave it is referring to.... oh well usual buggy mess i suppose
I tried Dewor3's solution and it wasn't working for me. RickyRick on Valhalla gave me this info which worked.
- Stand on the road outside of the cave. You have to stay outside of any "named landmark" zones. Just wait there and when the mobs spawn they will give you quest credit. If you are in a landmark like the cave you will not get credit.
I was teleporting while in front of that cave and the mobs spawned with a quest marker above them
The solution @Dewor3 has actually seem to be working. I went to the left of the cave entrance around the mountain, strolled around a bit and came back and then I got the objective to update when the npc's spawned in.
I went to the right of the cave a bit up the hill and came back, it seemed to have activated another objective to kill a few mobs outside and it was done
Seems bugged, entered the cave, and the objective 'Travel to the cave from the note' is ticked off, but no further progress is made. Cave filled with the spore mist at one point, but didn't seem to accomplish anything.
Check Dance of the Fireflies for the cave location. If you are stuck on Find the Cave task, go away from the cave and back to it and it will work. The area trigger is pretty big, and if you are inside it when you get the task, it just won't update (hence going away and back).