If you are living and working in the USA you are not an Australian resident for tax purposes.
Not true if you intend to return to Australia at some point and have Australian assets. If you own a house and it remains your property whether you rent it out or not you will be considered an Australian resident for tax purposes. There is also a factor of how many visits to Australia you make per year, which seems to be if you come back more than twice per year. There is a tool for calculating your Residency status on the link you provided. Entirely agree with getting professional advice though. The original question involved working in the US with income streams from Australia, that's where it gets tricky, having income or assets in Australia with evidence you intend to return at some point.