We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage phi and a magnetic field B.We investigate the interplay between the shift (omega(B)) of the Kondo peak in the spin-resolved density of states (DOS) and the one (phi(B)) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of B down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as phi(B) only for vertical bar g vertical bar mu B-B >> k(B)T(K). Our auxiliary master equation approach yields highly accurate nonequilibrium results for the DOS and for the conductance all the way from within the Kondo up to the charge fluctuation regime, showing excellent agreement with a recently introduced scheme based on a combination of numerical renormalization group with time-dependent density matrix renormalization group.