marami-rami na akong nababasa online once nag start na residency mo (i.e. the moment you entered Oz and stayed), any money you bring/transfer/receive to/in Oz earn worldwide will be taxable. the ATO can monitor your AU bank account, so alam nila yung pumapasok/lumalabas na pera.
meron rin exemptions though, like income na already taxed by a country that has a double tax agreement (DTA) with Oz. that agreement prevents you from paying taxes again in Oz. syempre, need mag provide ng proof for the exemptions when you file for tax returns at the end of the FY.
personal research ko lang naman ito hehe. my understanding may also be wrong.