My guess would be that there's a lot of shifting around that takes place after the May 15 deadline. One student being accepted off of a waitlist at a school that they prefer to the one they gave their May 15 "yes" to sets off a chain reaction, opening up a new spot at the school they withdraw from which is filled by another student who may give up the spot at their original school, and so on. Even though this shifting will continue to some extent until people start their first day of class, I'd assume the biggest surge of activity happens soon after the May 15 deadline. As a result, it probably takes a few weeks post-deadline for a school to get a clear idea of how many spaces they're likely to have open. If what Hotshy is guessing about looking at the waitlist in batches instead of on a rolling basis is right, this might explain why they wait a few weeks before they start accepting off of the waitlist.
For the record, the waitlist started moving in June last year, IIRC. They could be doing something different this year, or they could just be saying July to give a conservative overestimate.