Most payroll reports are based on pay periods, not the pay period dates.
The pay period shows when the employee worked. The payment date shows when the wages were paid. For reporting tax, STP, super and financial year totals, the payment date is usually the date that determines which month, quarter, or financial year the pay belong to.
Example: if the pay period is Monday 24th June to Sunday 30th June, but the payment date is Monday 1st July, that pay will usually appear in July and the new financial years reports. This is expected for work performed in June.
You do not need to change your pay period to make reporting line up with the month end. Keep the pay period as actual dates worked, and use the payment date when checking reports that are based on wages.