Your image is too large for the button. The problem is that it has to start compressing the tops and bottoms because the button has been squished smaller than the actual artwork. Try making that artwork for the square much smaller (at least as small as the button will be).
I have found that there is an issue with my method of doing this though on Mavericks and it doesn't want me to change the contentsCenter of the layer. However, it should still work.
Btw, thanks for watching the tutorial :)