They don't say when the draw is anymore, just that if you want to pull your name out it has to be withdrawn by the June 3rd. The draw used to happen around June 10th.
Why do you need funds in case you draw? WY you pay up front for the tags and they refund your money if you don't draw. Just curious. Start checking their site the week before they say the results will be available. They are usually several days early.