The definition of 'Post-Scrimmage Kick' refers to a set of conditions used to determine a special enforcement rather than a specific foul. For the 'Post-Scrimmage Kick' definition to be applicible, all of the conditions have to be met at some time during the down. This means some of the conditions can be met prior to, or after the actual foul and at least ONE of the conditions (the one requiring that K is not the next to put the ball in play) must happen after the foul.
Where we sometimes confuse ourselves is by referring to a foul as a "'Post-Scrimmage Kick' foul" when actually it is a "foul that occured in the midst of all 'Post-Scrimmage Kick' conditions being met".
My only real beef with the PSK definition is the fact that they've included the prefix "post-" unnecessarily. It implies a specific time frame that isn't accurate for when the conditions can be met.