jmark - our recent experience inbound - St. Thomas to Tortola via private water taxi we presented paper copies of our vaccine cards and negative test results to the BVI customs agent.
Outbound Tortola to St. Thomas via Cape Air we presented our vaccine cards and a digital copy (screenshot on our phones) of negative test result to the gate agent at EIS (Tortola airport).
We were still required to upload both items to the USVI travel portal to get our green QR code to enter the St. Thomas airport.
(this was our experience in the last 10 days)