Right. "Game registered" is the entering of your registration code into the account system. The paying for 90 days of game time can happen anytime between now and 2.0 release. (you might have wanted to quote the whole response, as the part you quoted is not the best part of the response)

May 31st was only the "buy the game" cut off date. It's NOT a cutoff for the paying for game time.
Those who input their FINAL FANTASY XIV-registration code (ie: CD Key or equivilant) by the 31st of May as well as pay the subscription for 90 days in advance after the end of the free trial period will fulfil the pre-requisites for the Legacy Campaign.