The location of a Trust (as an RFI) will depend on where the trustee(s) is resident. If the Trustee of the Trust is located in Barbados, then the Trust must register with Barbados and report its financial accounts there. The Trust will not register in the BVI. 

The settlor(s), Trustee(s), the protector(s) (if any), and the beneficiary/beneficiaries or class of beneficiaries, and any other natural person(s) exercising ultimate effective control over the trust (including through a chain of control or ownership), must always be treated as controlling persons of a trust, regardless of whether or not any of them exercises control over

Given the fact that settlors are listed because they exercise ultimate effective control over the trust, they will have to be named. In a case where they do not have such control then they are not an account holder.