The stone he put in its place looked nearly the same as Jon's stone (except for the barely noticeable white specks), but it wasn't. It was the Day Stone.
It worked just like the normal stone, but only during the day (anytime that the sun was up, so right after sunrise or right before sunset counted as day). If the stone was used during the night, then it would not glow as it normally does and it would not grant the wishes made with it. However, the moment the sun rose above the horizon (sunrise, in other words), any wishes made during the night 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 night, the wish wouldn't be granted until sunrise, at which time Karyn would appear wherever Jon was at that moment, whether it was in his bedroom, his bathroom, or some other place.
When the "delayed" wishes get granted at sunrise, 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 night.
