When Australian polymer banknotes were first printed, the signature of the Secretary to the Treasury appeared above that of the Governor of the Reserve Bank. However, from 2002 the signatures were reversed on new banknotes when they were printed. You can determine the year a banknote was manufactured by looking at the first two numbers of the serial number.
The order of the signatures is not a determining factor when assessing whether a banknote is genuine. Australia's banknotes have many features designed to combat counterfeiting and the Reserve Bank has produced a Counterfeit Detection Guide to assist the public to detect and deal with counterfeits.