Disclaimer: I'm not much of a portrait photographer, and have never considered the differences between dark- and light-skinned models in my limited lighting setups. Grain-of-salt, and all...

When adding light, whether with reflectors, off-camera flash, studio lights, etc., knowing and controlling the ratio(s) of the lights is important. The ratio between ambient vs. reflected light, key light vs. fill light, etc., determines how the highlights and shadow areas of subjects interplay.

Photographer Kyle Cong wrote about this exact subject on his blog: Portrait photography how to: Photograph darker skin tone with off camera flash (also picked up and re-posted by PetaPixel).

Being a portrait photographer and have been using off camera flash for many years, I used to think skin tone is irrelevant to portrait lighting setup. ... My first model has very pale skin, my lighting setup was perfect for the light effect I wanted. After I start photographing the second model who has darker skin tone, I realized that my first lighting setup is quite off. ... Lighter skin tone will bounce more light which makes the shadow harder to preserve.

For this reason, when photographing people with lighter skin tone, our light needs to be positioned so the shadow will be protected. ... To be more exact, the controlling of the ratio between highlight and shadow will be different.

... When placing a bright and dark subject right beside each other the bright subject will look brighter, the dark subject will look darker.

If we use our light on someone with darker skin tone in the same way as lighter skin tone, the shadow will look too dark (As I mentioned above, protecting the shadows). This will make the highlight appears brighter. So bright that they looks like hot spot even though nothing is over exposed. In other words the image will be too contrast. Lots of highlight and shadows but lack of half tone.

To fix this issue, we need to move the light a bit closer to the shadow side so part of the shadow will be lit as well. Remember just part of the shadow not all of them. Pointing the light directly at the shadow side will destroy your shadow and mess up your mid tone. The result will be a flat image with flashy look.

Cong's blog has several photos which demonstrate his approach and results of changing his lighting for darker-skinned models.