Super is required to be paid at least quarterly and within 28 days after the end of each quarter. Therefore, 28th July is the official due date for the June quarter super. It is possible to make more regular payments to assist your cash flow, however this is not required by law.
Deductions for super can only be claimed when super has been paid. If you pay prior to the EOFY (i.e. before 30th June), it is deductible in this financial year. However, if you pay between June 30th and July 28th, it is deductible next financial year instead.
This is important to consider when estimating your tax for the year because it is that your financials can be showing a loss yet you will be liable to pay income tax due to unpaid super at year end.
Super is only considered paid once it arrives in the employee's superannuation account, therefore you need to allow adequate time for the payment to process (up to five days). If you want to ensure your super is considered paid by 30th June, you should process the payment by 25th June!