As pointed out in the comments, this is not a good generalization.
You correctly stated that paramagnetic complexes have (at least) one unpaired electron, while diamagnetic ones have a closed shell. Your idea of colour is incorrect, what you describe is fluorescence. Generally speaking, we do not observe color because a compound emits light of a certain energy. We rather observe what is left from the light that shines on a compound. The absorbed part is the part we cannot see anymore.
Whether a complex is coloured or not depends on the energy difference of the ground state and possible excited states, and whether a transition between these is spin-allowed or not. If there is a spin-allowed transition that has an energy in the range of visible light, we observe a colour.
Consequently, there is no inherent connection between colour and magnetism.
I can, however, imagine how this coincidental correlation might arise: In complexes with an even number of d electrons, there is always the possibility to have a paramagnetic or a diamagnetic ground state configuration, e.g. the $d^8$ example in the diagram. When the orbital energy difference $\Delta\varepsilon$ is sufficiently small, the paramagnetic configuration will be the ground state. If it is large, the diamagnetic one is the ground state. The energy difference $\Delta\varepsilon$ also correlates with the energy of an electronic transition: the larger the difference, the shorter the wavelength we observe in a spectrum.
I assume that the energy difference at which the diamagnetic spin state becomes the ground state lies in the region where electronic transition have such high energies that their absorption does not happen in the visible region anymore and thus the complex appears colourless. This would justify what you found by connecting the electronic transition energy with the magnetism via an orbital energy difference.
I want to emphasize that an orbital energy difference is not the same as a state energy difference and serves purely as conceptual aid. Neither orbitals nor their energy differences are observables.