The cubic spinel CdCrS gained recently a vivid interest, given the relevance of relaxor-like dielectric behavior in its paramagnetic phase. By a singular combination of local probe techniques, namely, pair distribution function and perturbed angular correlation, we firmly establish that the Cr ion plays the central key role on this exotic phenomenon, namely, through a dynamic off-centering displacement of its coordination sphere. We further show that this off-centering of the magnetic Cr ion gives rise to a peculiar entanglement between the polar and magnetic degrees of freedom, stabilizing, in the paramagnetic phase, short-range magnetic clusters, clearly seen in ultralow-field susceptibility measurements. Moreover, the Landau theory is here used to demonstrate that a linear coupling between the magnetic and polar order parameters is sufficient to justify the appearance of magnetic cluster in the paramagnetic phase of this compound. These results open insights on the hotly debated magnetic and polar interaction, setting a step forward in the reinterpretation of the coupling of different physical degrees of freedom.