The stone he put in its place looked exactly like Jon's stone, except that it wasn't. It was the Displacement Stone.
It worked just like the normal stone, but after every wish, someone who was considered "close" to the wisher (relationship-wise) would be displaced - in other words, they would become part of a different family or become part of a different group of friends, without changing their personality or lifestyle too much. And in their place would be someone from a different family or different group of friends. It's not always a straight swap, though. One displacement could cause a chain of changed families or friends.
Only the wisher would notice any changes caused by the displacement. Everyone else would think that things had always been that way, and reality would also reflect that (family resemblance, photos of friends, etc.).
But these "displacements" weren't permanent. Once a person had been displaced, someone could wish them back, but since that's another wish, another person would be displaced.
