  We simulate the propagation of cosmic rays at ultra-high energies, $\gtrsim
10^{18}$ eV, in models of extragalactic magnetic fields in constrained
simulations of the local Universe. We investigate the impact of different
magneto-genesis scenarios, both, primordial and astrophysical, on the
propagation of cosmic rays. Our study shows that different scenarios of
magneto-genesis do not have a large impact on the anisotropy measurements. The
distribution of nearby sources causes anisotropy at very high energies,
independent of the magnetic field model. We compare our results to the dipole
signal measured by the Pierre Auger Observatory. All our models could reproduce
the observed dipole amplitude with a pure iron injection composition. This is
due to clustering of secondary nuclei in direction of nearby sources of heavy
nuclei. A light injection composition is disfavoured by the non-observation of
anisotropy at energies of 4 - 8 EeV.
