Try prying the cover off the S pen button and adjusting the sensitivity control:

http://forum.xda-developers.com/showthread.php?p=32908967

 

It is my understanding that you should have to touch the screen to control everything. My Spen on my Note 2 controlled everything while being inches from the phone and Tmo swapped or the entire phone telling me the Spen was defective. It was nearly impossible to use, when I would attempt to hover it would just open the file, it would open apps if I was just over the icon, it would cause Web pages to scroll and forget using the pen to write. It was a scribbled mes. I think your Spen is actually working the way it is meant to now.

 

I know for certain things you can hover your spen at the bottom or top and it will scroll the page up or down. Other then that I have no idea.

 

From reading this one and other threads about s-pen, turns out that you could control the "Force" by tuning the pot under the pen button cover. Or by whacking the tip of the pen on wall. Which ever method you prefer!

 

The first mode you speak of was a flaw in you spen. You were not supposed to have the ability to control everything without touching the screen.

It sounds like the "problem" fixed itself and the pen is working as it should now.

LOL. I don't think there is a way to "fix" this. There is nothing wrong.