We report on the experimental observation and theoretical studies of a self-assembled Fe-rich (In,Fe)As nano-lamellar structure that is driven by anisotropic spinodal phase separation at the growth front during laser heating-induced recrystallization of Fe-implanted InAs. Pseudomorphically embedded in the InAs lattice, those Fe-rich nano-lamellae are perpendicular to the (001) surface and parallel to the in-plane \([1\bar{1}0]\) crystallographic direction. Our findings explain the surprisingly high apparent Curie temperatures and unexpected eight-fold symmetry of crystalline anisotropic magnetoresistance (AMR) found previously in Be-doped \(n\)-type (In,Fe)As grown by molecular beam epitaxy. Prompted by these results we discuss how a different \(d\)-level electronic configuration of Fe in InAs and Mn in GaAs affects the magnetic ion incorporation and spatial distribution and, thus, magnetism, magnetic anisotropy, and AMR of these two magnetic semiconductors undoped or co-doped with Be.