I have never dealt with API as a former N.B. Boiler and Pressure vessel inspector, so if the PV (fired or unfired) is designed per ASME codes, naturally I would base my pressure safety valve and relief valves pressure setting and relieving capacity per ASME. If API codes were used in the fabrication of vessels than I suspect that the calculations would be based on API but from my standpoint I would definitely check with API to determine if I am correct.