I had an interesting interaction on my departure from Australia. I too have Australian and US citizenship. I flew SYD-MEL domestic then MEL-LAX and when I checked in Virgin Australia Domestic I gave my US passport and my Australia passport information was still in the system. When she tried to override it with my US information (to enter the US) it wouldn't work and the agent had to make several calls including to customs and immigration desk. She then told me that my US passport was new and my number wasn't showing and would need to link it to my old passport (whatever that means????) I just became a US citizen. She then asked me if I have traveled on my US passport before and said 8 international trips already... again didn't know what that had to do with me adding my US passport to the reservation. I will note she at no time scan my passport(s) only manual entry. I was at the check in desk for 35mins while she was trying to figure it out. She then had to call another number before someone came over with boarding passes for me and bag claim. This might have been isolated since I was flying Domestic before connecting to International. In the end it was sorted but confusing since there are so many dual citizens.
departure immigration at MEL E-gates my Australian passport came up as error and I had to go have an immigration officer manually exit me out of the country. But on entry into the US, I used global entry with my US passport without a hitch.