The stone he put in its place looked nearly the same as Jon's stone (except for the barely noticeable black specks), but it wasn't. It was the Night Stone.
It worked just like the normal stone, but only at night (anytime that the sun wasn't up, so right after sunset or right before sunrise counted as night). If the stone was used during the day, then it would not glow as it normally does and it would not grant the wishes made with it. However, the moment the sun went over the horizon (sunset, in other words), any wishes made during the day would be instantly granted. But they would be granted as if they were wished at that specific moment.
So, if Jon said "I wish Karyn was here," but during the day, the wish wouldn't be granted until sunset, at which time Karyn would appear wherever Jon was, whether it was in his bedroom, the bathroom, or some other place.
When the "delayed" wishes get granted at sunset, it doesn't matter if anyone is touching or anywhere even close to the stone. The delayed wishes would get granted to whoever made them during the day.
