If you do not see the Nine Tail NPC at the marked position in Payon Cave 4, you have to find the Nine Tail that is related to the quest and kill it.
The Nine Tail related to the quest is just like any other Nine Tail. So you might have to kill all Nine Tails in the map, fortunately there are only 3 of them and the chosen one should be relatively close to the marked spot. When the Nine Tail that is related to the quest is killed, a Nine Tail NPC at the marked spot will appear.
When talking to it, choose "Nodding" in the menu option. (If you choose the wrong option the NPC will disappear. In that case, you will have to wait 5 minutes for the chosen Nine Tail to respawn and kill it again.) It will give you a /hmm emotion, talk to it again. This time he will tell you about the quest (or if you have the items, it will create the mask for you). After talking, it will disappear again. Just wait another 5 minutes to have the chosen Nine Tail respawn at the marked position and kill it if you need to talk to it again.