The Operational Regulations for the Cayman Islands are the Overseas Territories Aviation Regulations (OTARs); in this case Subpart K of OTAR 91 and 135. The rules in those Subparts place obligations upon the pilot and the operator.
The relevant rules can be found on the ASSI web site:
http://www.airsafety.aero/assets/upl...135_121_v6.pdf
When considering these rules be aware that they are cumulative - i.e. the operator has to apply the elements of both Part 91 and 135.
The actual conditions in the Scheme will be those approved by the Governor of Cayman Islands (approved by the Cayman CAA) when the AOC was issued.
As the OTARs are objective in nature, it is likely that the Scheme will have been based upon guidance produced by another State - which is likely to be the CAA, FAA or TC.
Jim