assuming the traffic laws in Australia were more like those of the USA

Maybe there's some part of America where you have to stop before entering a roundabout. The country is fucking insane in many ways so I wouldn't be surprised if there's an exception somewhere. But it's definitely not the norm.

To be fair, in one clip (from memory I think it was 5?) the postie really didn't do himself any favours by looking in the opposite direction to where the car was coming from, so he reacted way later than he would have.