I'm still at 4/24 - 5/8 as well but I'm pretty confident this means delivery on the 24th! You can already reserve a spot for an Apple Watch Workshop in the Apple Retail Stores, which should be an indicator.
The description mentions to bring your Apple Watch. Why should they arrange these workshops if nobody gets his or her Apple Watch until that date? The workshops start 4/24
So I guess for most of the 4/24 - 5/8 people this means Apple Watch very soon. To my knowledge there is nobody with a 4/24 delivery - everyone seems to have 4/24 - 5/8.