No, no test is required to return to the mainland US from the US Virgin Islands.

If you’re ready for a tropical getaway and looking for the least amount of challenges when traveling, the US Virgin Islands (USVI) should be #1 on your list. Based on the latest travel requirement by the Centers for Disease Control and Prevention (CDC): starting January 26, 2021, all international air travelers coming into the US, even US citizens, and regardless if you have been vaccinated or not, are required to present a negative COVID-19 test result taken within 3 days before your trip or documentation of recovery from COVID-19 before you board a flight to the US. Because the USVI is an American territory and on US soil, the new CDC requirement does not apply for travel directly between the USVI and the US mainland.

Testing and International Air Travel | CDC
USVI Update | Press Release 
USVI | COVID-19 Traveler Screening Tool