I don't know of a ASTM test on compatibility. What I can say is that alkylbenzenes exhibit poorer properties than PAOs as rolling and drawing oils for copper. However, their excellent solvency and low pour point make them suitable to operate in arctic greases, gear oils, hydraulic and power transmission fluids. The most widespread use is, however, as refrigerator oils.
Alkylbenzenes are fully compatible with fluorinated refrigerants (such as R22 and R502) whereas mineral oils may suffer from wax precipitation and PAOs give phasing problems. Normally no additives are required, but in severe applications anti-wear compounds such as triaryl phosphates have been succesfully used.
The natural solvency of the alkylates is beneficial to minimising the formation of sludges, varnishes and other deposits.
A final application of the lower MW alkylbenzenes, alone or blended with mineral oils, is in transformer oils, where high resistance to gas evolution is required.
Buena suerte.