Not saying what it is or isn't for your birds, but vitiligo in poultry does not impact the deposition of carotenoids in the skin, for the record, only the deposition of melanin. Smyth line birds were bred from Brown Leghorns and had yellow skin even after their vitiligo was triggered.
If you had looked further into this than just the surface level, you would have also found that early stages of vitiligo do not always fluoresce. It has to do with a protein in the skin that absorbs the wavelength of light that eventually is no longer present in the skin where vitiligo is impacting it, but sometimes is still present in early stages of vitiligo. You also would have found that there are other skin conditions that impact whether that protein or other pigments are present in the skin or not, and that individuals with those other conditions will also fluoresce at impacted sites, so it's not just vitiligo that glows under a blacklight. It says as much in the link you posted. Any spot with a complete lack of pigmentation caused by
any condition will fluoresce because that area of skin is lacking those proteins and pigments that absorb the wavelengths of light from a blacklight and so it instead reflects that light, making it look like it's glowing.
This is why chickens who have white patches on them, not as a result of vitiligo but simply from their normal patterning, will fluoresce under a blacklight as well. The black light just shows you the patches that are lacking pigments that would otherwise absorb the light, as in from one of the white genes or from silver.
View attachment 3703804View attachment 3703805