We studied the overall atomic mobility of sodium bis-(2-ethylhexyl) sulfosuccinate (AOT) reverse micelles in deuterated cyclohexane (C6D12) as a function of the molar ratio W=[D2O]/[AOT] with an incoherent quasielastic neutron scattering experiment at high energy resolution. For the almost anhydrous sample, the quasielastic broadening can be entirely attributed to the reverse micelle global motion, by considering explicitly both the rotational and the translational terms. As W increases above a threshold value W approximately 1 a wide quasielastic signal appears, which has been interpreted as the onset of a hydration-dependent intrinsic micelle dynamics. Such a contribution, which involves the AOT monomer hydrogen atoms, has a characteristic time of 0.2 ns. This result has been compared with previous dielectric measurements, which detected a relaxation process of the AOT fully hydrated head groups with the same characteristic time. The internal macromolecule mobility evaluated as a function of W numerically correlates with that of the mobile head groups, calculated by dielectric measurements. These findings suggest that both the hydrophobic and hydrophilic moieties dynamics is activated by the progressive hydration of the reverse micelle.