To be legal, you need a visa that matches the activities you´re performing: work, study, tourism, etc. Showing a Dominican cedula is not always enough, as there are many cases of people with fake or bought cedulas. I remember this guy with a Dominican cedula but a heavy creole accent. It was not only the accent but the way he spoke Spanish. Although his cedula had common local names, and he claimed that he was born and raised here, that both his parents were also born and raised here, and had no ties to Haiti., but couldn´t explain the accent.
I know a few legal Haitians, for instance, my former teacher of french was Haitian and taught at a language academy. He was also hired by the Board of Education and appeared on many instructional educational videos that aired during the pandemic. He was with a work contract, later he got into the regularization plan. I also had a Haitian friend who had a registered business here, and another one who came here on a student visa.