Coriolis effects, induced by the molecular rotation, on doped helium clusters are unravelled by calculating the vib-rotational Raman spectra of (3,4He)4-Cl2(X) clusters as a function of the temperature. Quantum Chemistry-like calculations using the Full-Configuration-Interaction Nuclear-Orbital approach reveal the key role of spin-dependent couplings in fermionic clusters at very low temperatures (0.07 K) for the first time, signaling the effective decoupling of the spin angular momentum from the molecular rotation. On the other hand, the spectra of bosonic (spinless) (4He4)-Cl2 clusters are almost unperturbed by Coriolis couplings at the considered temperature range (1-0.37 K).