The stone he put in its place looked almost exactly like Jon's stone, except that it wasn't. It was The Initial Target Stone.
It worked just like the normal stone, except that the wishes would always affect the same person as whoever was affected by the first wish, no matter if someone else was specified in the wish.
For example, if Jon's first wish was about himself, then every other wish after that would affect Jon, whether he specified himself or not. If Jon's first wish was about Karyn, then every other wish he made after that would affect Karyn, whether he specified it or not.
Now, if Karyn used the stone after Jon used it, then her first wish would be granted exactly the way she wants. But then every other wish afterward would only affect whoever the subject of her first wish was.
For every person, the subject of their initial wish will be the subject of every wish thereafter, no matter whether they specify someone else or not.
