I actually purchase the same case, but a different [glass] screen protector;
Amazon.com: Tech Armor Samsung Galaxy S4 SIV Premium Ballistic Glass Screen Protector - World's Clearest Screen Protector - Retail Packaging: Cell Phones & Accessories
The case is great, and so was the screen protector ... eventually.
I applied the screen protector in the bathroom after the hot shower had effectively fogged up the entire mirror - not sure I would recommend that. I followed the directions religiously, but found I had a few small areas, and two fairly large areas that just didn't seem to stick. Don't take this prior statement lightly, I was extremely disappointed at this stage and about ready to throw in the towel and order up yet another glass screen protector ... anything that wasn't going to look this terrible! (see a couple posts down for the image of how bad this looked, initially)
After trying to squeegee those spots out, I just couldn't get them to STAY out but I did notice that they COULD be eliminated if I pressed my thumb hard over them, but they would always return in a few seconds. I grabbed some very soft tissue (toilet or Kleenex) and folded it into a square. I then ripped off some small sections, about the size of the portion of the screen protector that wasn't staying the way it should. After applying a little scotch tape to those pieces, I lightly stuck them to those respective areas of the screen that didn't seem to take properly.
I found that flattest solid surface/table I own and put a sheet of printer paper on it, laid the phone on it, face down (with those pieces of tissue stuck to it in those strategic locations where I needed some focused pressure). I put a paper towel over the phone and stacked 10 lbs. of exercise weights on top of the phone (do this very carefully, at YOUR OWN RISK). It sat there like that for about an hour, and came out perfect. The only way you can tell the glass screen protector exists is by seeing it's edges around the perimeter of the phone.
Quite happy with the results.