As others have said, there are no official Star Wars days at DLR. There are a few days when it seems like Star Wars fans may choose to try and meet up in the parks. I've seen April 16-19 listed (coincided with the Star Wars Celebration VII at the Anaheim Convention Center, May 4/5 for May the Fourth/Revenge of the Fifth, and the Star Wars Half Marathon in January).
I hadn't heard about the June date before, but it's good to know, even if they don't seem to have an event planned this year.