I just did a book signing at Barnes and Noble and I got the most detailed info (more detailed than the website or the poster outside the store) from calling and speaking to a live person. It could be a typo and they meant June 4th or they could just be unclear. It could be that you CAN buy the CD starting June 3rd (which is when it is released) and then the wrist bands are being given out starting June 4th. Usually they don't care when you buy the CD as long as you have the receipt that you got it from Virgin. They make the money anyway!
I have been to only one CD signing at the Virgin Megastore in the past but it was a little different because the CD actually didn't come until the day AFTER the signing. You can to go in the morning, pay for the CD, they just gave you the inside booklet for the signatures and then you could go the next day - after the signing was already over! - to pick up the actual album and the plastic jewel case.
I'm hoping to get a chance to go to this although I can't commit for sure since various aspects of my life are in limbo right now. Anyway, if you call, please report back any info you find out. Thanks!