As a naturalized DR citizen and a born USA citizen, I have to exit the DR using my USA passport if I am going to the USA. I know this because they made me change my E-Ticket on departure for my last USA trip.As a naturalized Dominican citizen, I have to exit and enter DR using Dominican passport. In some countries I travel to, I show another passport on arrival for visa-free entry, but that has nothing to do with the subject of this thread.
I can re-enter on my DR passport, because I now have one, but if I didn't I could enter on my US passport. I was under no obligation that I know of to get a DR passport when I was naturalized.