We argue that the enhancement in the spin polarization of anti-hyperons compared to the polarization of the hyperons in noncentral relativistic heavy-ion collisions arises as a result of an interplay between the chiral and helical vortical effects. The chiral vortical effect generates the axial current of quarks along the vorticity axis while the recently found helical vortical effect generates the helicity flow -- the projection of the quark's polarization vector onto its momentum -- along the same axis. For massless fermions, the helical charge corresponds to a difference in the contributions of particles and anti-particles to the axial charge. Assuming that the spin of light quarks transfers to the strange quarks via the vector kaon states ("the spin-vector dominance"), we are able to describe the ratio of the (anti)hyperon spin polarizations, obtained by the STAR group, without fitting parameters.