Order of filling electrons in Jahn-Teller energy diagram When filling electrons in atomic or molecular orbitals we fill first the lower energy orbitals and then the higher, according to Pauli and Hund's rule. But this seem not to be the case when considering metal complexes. According to Wikipedia

For example why the $d_{xy}$ orbital in the $d^4$ high spin is not fully occupied? Is the pairing energy that changes the order of filling the orbitals?
This was just an illustrative example. The tendency of a complex to favor low-spin or high-spin configurations is dictated by the relative magnitudes of the pairing energy, P, and the splitting energy, $\Delta$, between $e_g$ and $t_{2g}$.*

If $\Delta$ is greater than the energy required to pair two electrons, then electrons pair in $t_{2g}$ before occupying $e_g$. In the example you've shown of compression, this would be the $d_{xy}$ orbital.

*For octahedral complexes. Jahn-Teller can also happen for tetrahedral complexes.