Certain places and strangers use a phrase like, "…will give the first character who visits [something good] then vanish to the discard pile" I've been playing that when that phrase is used, it means that it doesn't apply to the character who drew the card. It seems to me that it is intended to be the reward for the character who manages to get there next by whatever means.
On a similar vein, The Phantom and Ritual Master get a number of cards placed upon them. "Once per visit" a card may be taken. Does the character who drew The Phantom get to take a card, or are these cards intended for subsequent visitors?