Once you have lodged your tax return it will come in with your return. Its usually not two separate payments. So on your bank statement it wont be $xxx Tax return PLUS $600, It will be one lump sum.
If you don't need to lodge a tax return you need to inform the family assistance office.

Also, it wont happen till both you & your partner have lodged your returns (or notified them on a non lodgement)