The US Virgin Islands does have their own criminal code, and the Superior and Supreme courts of the Virgin Islands hear cases related to it (the District Court is a federal district court). However, while I haven't looked at the specific facts in the case against him, I'm sure Mr. Epstein was accused of human trafficking that crossed state and probably national borders, which puts it squarely in Federal jurisdiction. Based on COMMONWEALTH OF PUERTO RICO v. SANCHEZ VALLE, most likely the dual sovereignty doctrine would not apply in due to the Virgin Islands being a territory - if he committed crimes in a particular state, that state could separately prosecute him for those crimes regardless of the Federal indictment, but in the cited case the Supreme Court of the United States ruled that
The Double Jeopardy Clause bars Puerto Rico and the United States from successively prosecuting a single person for the same conduct under equivalent criminal laws.
In theory, Virgin Islands criminal violations which were sufficiently different from the US federal government indictments could be tried in their Superior Court, but more likely would be included in the Federal indictment.