No.
NAR S&T, TRA TMT and CAR MTC are simply recognized certifying authorities. We are disinterested third parties who witness a small number of manufacturer supplied hobby rocket motors motors in operation to make sure they meet the manufacturer's supplied specifications when operated according to the manufacturers directions.
The manufacture supplies a certain number of motors as specified in NFPA 1125, and their specifications. The testing organizations assemble and operate the motors on an instrumented test stand and observe the motor burn and collect the test data and compare what was obtained on the test stand to what is required under NFPA 1125 for the manufacture's motors to meet their own specifications. If the motors perform as the manufacturer specifies, they pass certification testing. If they perform outside the specified specifications, or one catos, they do not pass certification.
It's really that simple.