He is a US citizen which I believe disqualifies him from running.
Apparently, that doesn't apply to him and has been the argument he has been using (with the consultation of lawyers specialized on citizenship matters in the DR) since he started campaigning. When the JCE didn't recognize his political party during the last elections, it was based on the 10 consecutive years permanent residence in the DR requirement and not on the dual nationality front. Now he complied with that requirement, so the JCE can't object to recognizing his political party, as has been done.
Unlike 99.9% of the Dominicans that were born in other countries and upon birth were granted citizenship of said countries, the Trujillo family is the only one that by law were prohibited from being in the DR. It was during the administration of Hipólito Mejía that that law was derrogated by the president himself and parts of the Trujillo family began to return and establish themselves in the DR. The fact that they began to return as soon the law was eliminated show that they wanted to return previously but couldn't. Most aren't in the limelight like Ramfis or Aida, so they literally move among the people (including expats in places like Cabarete, Santo Domingo, Punta Cana, Juan Dolio, etc) without ever knowing that they are descendants or related to Rafael Leonidas Trujillo. People don't how how widespread is the influence of members of the Trujillo's in the DR. For example, there is a very popular Dominican shoe store that very few people know there is a member of the Trujillo family involved in the managerial positions (and they could be one of the investors of the company, though I'm not 100% sure of that.) The store is very popular with Dominicans all over the DR, but 99% of them have no idea there is a Trujillo involved. The same happens with many other companies in many other sectors. For now, Ramfis is the only Trujillo member that is involved in politics, but this could be the beginning of more widespread Trujillo involvement in Dominican politics since Rafael Leonidas Trujillo was killed and months later all Trujillo's left the country and had all their properties confiscated by the Dominican government.
Anyway, the law that prohibited the Trujillo's from being in the DR meant that upon the enactment of that law all Trujillo newborns had to be born outside the DR. Angelita Trujilolo herself would receive personal friends she had living in Santo Domingo when she lived in Europe and later in Miami and still gets emotional when commenting about the part when her friends had to return to the DR and she stayed behind not for not wanting to go, but because she was prohibited. Before Hipólito Mejía removed the law prohibiting the Trujillo's from being in the DR, Joaquín Balaguer gave some of the Trujillo temporary permission to be in the DR and not be arrested in violation of the law that directly prohibited one family from being in the country.
That's the basis of the argument that Ramfis Trujillo didn't inherit US citizenship due to the will of his mother, but rather because she had no choice to give birth to him outside the DR. The Trujillo's couldn't transfer Dominican citizenship via jus sanguini, as such it was impossible for any Trujillo to gain Dominican citizenship, not even through naturalization.