payments scheduled on 4/15 but appear later in bank statement

I asked the same question recently at NAEA members-only web-board. Not a lot of responses, but one confirmation that EFW (electronic funds withdrawals) scheduled on a return filed on 4/15 seem to be considered timely even though not taken from the bank until one or two business days later.

IRS provides only one slightly vague statement at the web site:

"After the return due date, the effective date for EFW payments is the date the return or form is successfully transmitted."

This seems to imply that just like a paper mailed check, it is the (electronic) postmark date, not the date it clears your bank, that counts for the payment to be considered timely.