I find this paper interesting. This is where Bertlmann is wearing complementary coloured socks? I have a number of paintings on the go using colour complement pairs only: some crimson/viridian, some ultramarine/burnt sienna and one is yellow/violet. The advantage in painting is that it is simpler just using two colours. Adding the two colours for exactly complementary pigments gives a good black. In oils you need to add white in order to get any tone of grey. In water colour you just add water to dilute the black to grey.
But that is for pigments. There are different complementary colours for light (rgb) than for pigments (ryb). The three primary light colours are red, green and blue. A further complication is that the wavelength does not define the primary colour. A particular wavelength will trigger the brain to see a particular colour but the receptors can be triggered by a range of wavelengths. So I am not sure how complementary light colours can be exactly defined? I only paint in pigments.
I get lost in the calcium cascade due to my complete unfamiliarity. The two wavelengths are not meant to be complementary except in the sense that you only get one wavelength or the other. However, for SPDC, the two paths produce complementary polarisations. But not different colours? I do not see how the two colours, if that is what happens, are necessarily complementary? If they were different colours, I can see that energy imbalance of the photons could arise, but compensatory energy would be taken up by the emitting framework?