Orbitals are often imagined as independent from an other, filled or not with one or two electrons. This image is comfortable, but not accurate.
One first departure from this image is the electric repulsion between the electrons. If two electrons are closer to an other as a mean, this combination is energetically less favourable.
An other departure results from the fermionic nature of electrons. This reaches farther than the exclusion pinciple. The wave function of the set of electrons must be antisymmetric (including the spins), which shapes the orbitals. Figures for helium, with two electrons on varied orbitals, spins parallel (orthohelium) and antiparallel (parahelium), therehttp://hyperphysics.phy-astr.gsu.edu/hbase/quantum/helium.html
Notice the energy difference, in the order of 1eV. Interaction of the magnetic moments explains only about as much as the fine structure does, that is, far less.