That means we can expect a HUGE closing traffic jam at the end of the month. If you are refinancing or buying and expect to close during June, plan to close as soon as possible. Please try to close in the first half of the month if you can because closing during a volume crunch is not pleasant. There can be document or funding delays. You won't get a great selection of time, dates or location.
It's entirely possible that homebuyers have managed to close early and we won't have a last minute panic but why take the chance? If you can manage to close before the last week of the June, well I'd advise doing it. ;)