income

It depends on whether you are a bona fide resident of the U.S. Virgin Islands.  If you are a U.S. citizen (or resident alien), part of your income is taxed by the U.S. and part is taxed by the USVI; you will need Form 8986 at this link to figure the amount of U.S. tax allocable to the USVI.  TurboTax does not support Form 8986, so you will need to manually complete this form.  Community user DS30 has provided detailed instructions for how to file the two tax returns you need to file.

According to the IRS at this website about Individuals Living or Working in U.S. Territories/Possessions, an individual who has income from the U.S. Virgin Islands (USVI) will probably have to file a tax return with the tax department of the U.S. Virgin Islands. This website goes on to instruct that:

"It is possible that you may have to file two annual tax returns: one with the USVI tax department and the other with the U.S. Internal Revenue Service. You should ask for forms and advice about the filing of territory tax returns from that territory's tax department and not the U.S. Internal Revenue Service." (emphasis added)

Tax treatment also depends on whether you are a U.S. citizen or a "Bona Fide Resident" of the USVI.  See this IRS website for more on the taxation of people employed in the USVI.

In general, In general, according to IRS Publication 570 at this link, bona fide residents of the USVI pay taxes only to the USVI and U.S. citizens or resident aliens (but not bona fide residents of the USVI) with USVI source income pay a portion of the tax to each jurisdiction.