As far as I know, that's not how it works here.
Immigrant -> citizen -> taxed like the rest of us.
However, you could argue that immigrants are often destined for lower earning jobs which are taxed less on a proportionate percentage basis, but there are plenty of Australian-born folk working in that same tax bracket, so it's certainly not a 'immigrant only' thing here.
Having said that, my father in law to be was born in Australia but his folks were 100% Italian and still don't speak English well (if at all, I'm not sure).
I don't know how well his parents did but I know that he is absolutely rolling in money.
He owns a successful painting business and paints the houses of all of the rich and successful people in Melbourne. He's that good that people offer to fly him up to bloody Queensland, pay for his accommodation whilst he paints their house.... not to mention an exorbitant bonus for his trouble.