That clause is to be used in conjunction with the following:
The problem is that this year because the season is lasting longer than usual, the dates are all messed up between end of season, arbitration period, and free agency. But the gist of it is, teams have a limited time between the end of season and the start of free agency to affect compliance buyouts. To qualify, the player must have been on the Reserve List of said club as of the most-recent trade deadline.
The compliance period normally begins the latter of either June 15th or 48 hours after the playoffs end, and goes until June 30th. But this year, it starts 48 hours after the playoffs end and concludes on July 4 at 5 p.m. On July 5th, Free agency opens.
Hope this helps. Here's the link to the summary of terms if you want it:
http://www.nhl.com/nhl/en/v3/ext/CB...ummary_of_Terms_FINAL_-_Jan._12,_2013 (1).pdf
The bold part in the last quote, says the second buy-out period.... this would be the first no?