I have a June UY, too. Our 2012 UY goes from June 1, 2012 to May 31, 2013.
If you bank the 3 points, they will then be good for use from June 1, 2013 until May 31, 2014. So if your next trip is before May 31, 2014, you can use them. If it is after, they will be lost. Hope this helps!