So I asked Starlink support about the Dish and Obstruction Checker...
Happy Monday! Thank you for supporting Starlink during Starlink's Beta program. Great questions. You are right. As you are in the Southern Hemisphere, your Dishy will be pointing South. As we are currently in Beta, our app by extension is also in Beta and that is why you might be experiencing the Check for Obstructions Tool pointing North. If you have any other comments or concerns, please feel free to respond back to this ticket. Enjoy the rest of your day!
So yes, the Android app is wrong, and Dishy will face south.