Another way to look at the transition in electronic configuration is to consider species with the same number of electrons but different numbers of protons.
Start with $\ce{Cr^0}$ with its electron configuration $\ce{[Ar] 3d^5 4s^1}$. We add a proton to make $\ce{Mn^+}$, throwing in any necessary neutrons to keep the nucleus stable. We repeat this process to make $\ce{Fe^{2+}},$$\ce{Co^{3+}}$, etc., and eventually we get to let us say, $\ce{Xe^{30+}}$. In all these species the electromagnetic interactions between the 24 electrons are intrinsically the same, but the excess positive nuclear charge is building up and is bound to overwhelm the electron-electron interactions at some point. By the time we get to the huge excess positive charge in the xenon ion above*, the orbitals become roughly what they would be with isolated electrons, like the familiar hydrogen spectrum multiplied by the effect of a greater positive charge. The 3d orbital energy level sinks down to meet its shell-mates at 3s and 3p, leaving the higher-shell 4s orbital at a higher level. (* -- actually XPS binding energy data reveal that $\ce{Br^{11+}}$ already shows this effect.)
So at some point the outer electrons all fall into the 3d orbitals and the electronic structure shifts from whatever it was in the neutral chromium atom to $\ce{[Ar] 3d^6}$. In my example I predicted that we might have to go all the way to $\ce{Xe^{30+}}$ (or maybe $\ce{Br^{11+}}$ given the above-cited XPS binding energy information) for this transition, but in reality the 3d and 4s orbitals are so closely balanced in the first row of transition metals that we need not go that far. Adding two protons, and a few neutrons for nuclear stability, to chromium is enough.