The payment of a dividend via due bills is quite unlike a normal dividend payment. Shares that are purchased after the record date but before the deferred ex-date (the due bill period) are traded with a due bill attached.
The chain of events that begins on the payment/ditribution date works like this: The dividend is first paid to the shareholder of record, then, on the due bill settlement date, which is commonly two trading days after the ex-date, the dividend is withdrawn from the account of the shareholder of record who sold the shares during the due bill period and is then paid to the shareholder who owns the shares the day before the ex-date.