I’m not sure if you are correct about all the passports are connected. I was born in Taiwan and immigrated to the US when I was 14. I waited till I became a US citizen and got a US passport before I went back for the first time. I have gone back 10+ times with my US passport since and never had to deal with any issues exiting. I’m always treated as a US citizen even though I was born a Taiwanese citizen and my first passport was Taiwanese.