Just as a clarification, the RDFIs cannot, of course, post the funds any quicker than the ACH items themselves are received. So if the company payroll in question is not actually even originated until the 15th, then the RDFIs cannot post the funds until the opening of business on the 16th. (The ODFI sends the items out on the 15th, and the RDFIs receive them later in the day on the 15th or on the morning of the 16th, depending upon the timing of the ODFI's release and the receiving cycle of the RDFIs--one daily file, for instance, versus two or three. Even if the ODFI sends the payroll items out on the early morning of the 15th and the RDFIs pick them up in the afternoon, the receiving banks might not get their settlement through the Fed until the next day, and they aren't obligated to make the funds available to the receivers on that same day in such a case.)
Of course, under some scenarios the RDFIs will be memo posting some of the ACH transactions, so even if they receive them late on the 15th but aren't releasing them to hard post to DDA until the 16th, there might be a memo post distribution in the evening of the 15th that would make funds available via ATMs and might also counteract NSFs on check clearings.
As always, there are my opinions only.