  Recent core-hole-clock experiments [Phys. Rev. Lett. $\textbf{112}$, 086801
(2014)] showed that the spin dependence of electron injection times at
Ar/Co(0001) and Ar/Fe(110) interfaces is at variance with the expectations
based on previous calculations for related systems. Here we reconcile theory
and experiment, and demonstrate that the observed dependence is rooted in the
details of the spin-split surface band structures. Our ab initio calculations
back that minority electrons are injected significantly faster than majority
electrons in line with the experimentally reported ultrashort injection times.
The dynamics is particularly sensitive to the size (in reciprocal-space) of the
projected band gaps around $\overline{\Gamma}$ for both substrates at the
resonance energies. A simple tunneling model incorporating the spin-dependent
gap sizes further supports these findings.
