It has recently been suggested that two counter-propagating, circularly polarized, ultra-intense lasers can induce a strong electron spin polarization at the magnetic node of the electromagnetic field that they setup (Del Sorbo et al 2017 Phys. Rev. A 96 043407). We confirm these results by considering a more sophisticated description that integrates over realistic trajectories. The electron dynamics is weakly affected by the variation of power radiated due to the spin polarization. The degree of spin polarization differs by approximately 5% if considering electrons initially at rest or already in a circular orbit. The instability of trajectories at the magnetic node induces a spin precession associated with the electron migration that establishes an upper temporal limit to the polarization of the electron population of about one laser period.