Given that there are now three shows in The CW’s superhero multiverse that mess with time and routinely wind up with unintended consequences, perhaps the extra day in June is a result of somebody in the West-Allen family taking some liberties with the timeline, the Legends fumbling in their new mission from Constantine, or maybe even Supergirl trying to fix the mess she made at the end of her third season, although that mess may be contained to Earth-38.
If you did a double take when you saw that date, you weren’t the only one.
June is, of course, a month with only 30 days, so either the person who created this image made a mistake and nobody noticed until after Marc Guggenheim had already posted it or something is up with the Arrow-verse.