The ab initio Korringa-Kohn-Rostoker method combined with the coherent potential approximation (CPA) was employed to investigate the electronic, magnetic, and transport properties of medium-entropy face-centered-cubic (fcc) NiCoMn solid solution alloys. By comparing the CPA electronic structure with that from supercell calculations, we uncovered an unconventional CPA ground state, which correctly distinguishes two equally populated Mn CPA components—with large spin moments but opposite orientations. Using the spin spiral calculations, we further demonstrated that this ground state is most energetically favorable in the presence of spin noncollinearity, and no significant longitudinal spin fluctuation is observed, justifying the applicability of the Heisenberg model. The finite-temperature magnetism was further studied using different approximations based on the Heisenberg model, and we found the Mn moments to be fully disordered at low temperature due to a small net effective Weiss field on Mn. In addition, the magnetic effect on the electron scattering at finite temperatures was evaluated and compared with other scattering mechanisms. Since the magnetization-induced electron scattering is almost saturated in the ground state, (full) spin disorder only yields a small addition to the resistivity, whereas the thermal displacements increase it modestly. Finally, we elucidate the role of hydrostatic pressure on the magnetic and transport properties. These findings reflect the importance of the magnetic signatures on the physical properties of alloys, and they provide a window into magnetism-controlled electronic structure and energy dissipation.