I have a Note 2, but I'm not seeing the same thing you are.
Just to be clear on what is happening. You're using your phone and are in some app, you don't do anything for a bit and the screen turns off, and when you press the power or home button to wake the phone up you immediately see the recent apps screen?
Have you turned off the lock screen option?
Have you installed any custom launcher?
I have mine set so that a quick double tap of the home button will bring up the recent apps screen, and I think I set this via my custom launcher settings, but can't recall for sure.
I'm curious to see what is causing this, because I might actually like it if my phone woke up to recent apps.