A likely cause is metamerism: some colors can look one way to your eyes under a given light source, but reproduce differently to a camera sensor. In other words, the makeup may have appeared correct in person yet photographed much lighter or shifted in color.

That makes this more of a makeup/light-spectrum compatibility issue than simply “flash too strong,” especially since overall facial exposure was already close to correct. Certain pigments, cosmetics, and dyes can react unpredictably under photographic lighting and with camera color rendering.

So the problem may not be your setup alone. The makeup products themselves may not have been ideal for photography under that light. A practical fix is to test the exact makeup under the intended lighting and camera before the shoot, and adjust products or color intensity as needed.