The date you indicate for your money to be debited serves more as a "not before this date" than a "take it on this date". State returns often take longer to process, and your state return may not have been processed in time to make your April 1 payment date.
However, sometimes if they miss this date, your state will not take the money at all, lest you not have the funds available. I suggest that you contact your state and see what they say. If your account has not been debited by April 12, you may wish to make another payment. Your state will refund the excess if you end up paying twice, and you don't want to get stuck with a penalty for failing to pay.