The stone he put in its place looked exactly like Jon's stone, except that it wasn't. It was the Mimicry Stone. It worked just like the normal stone, except that every time the stone was used, a part of the personality of the one making the wish would change to mimic a part of the personality of the person closest to him. And after 10 wishes, the wisher's original personality would be gone, replaced by whatever personality traits were mimicked.
It's a bit complicated, so here's an example:
If Jon made a wish while standing near Karyn, then 10% of his personality would become like 10% of Karyn's personality. If Karyn loved horses, then that might be the part of her personality that Jon mimics. And then he would love horses too.
If he made all of his first 10 wishes near Karyn, then after the tenth wish, he would dress, think, act, and talk just like Karyn. However, if his first 10 wishes were near several different people, then he would dress, think, act, and talk according to the combination of all of his mimicked personality traits.
Every time a part of the wisher's personality gets changed, he or she won't notice it, as they would think that they had always been that way. But others will notice.
Once the wisher uses the stone 10 times, the function of the stone becomes like that of the normal wishing stone ... but only for the person that had already wished 10 times.