Since this seems to be coming up in DHT every 20 or so minutes, I figured I'd try to clarify things a bit. The story which was available starting yesterday is Season 2, Chapter 3, part 3. This is the last section which needs to be completed in order to get the 50% moogle. The moogle WILL NOT automatically be sent to you like the one for completing season 1, as this is a special event surrounding the 2nd anniversary. The moogle will be sent out to all players who complete the story to this point by September 1st, so it will not be sent out until after the deadline. Since Gumi will have to check who made it to the cutoff point by the cutoff date, I would guess probably the second week of September the moogle will be sent out to everyone who qualifies.

Edit2: The end of the chapter is after Road to the Village of Whyt-True Form. There is a cutscene spoiler:

Once you've seen that scene you are eligible for the moogle.

Edit: looks like someone asked in the DHT almost exactly 20 minutes after I posted this. Kinda made me chuckle.