I have a medium skin tone but tan very easiy. When I do, however, I get random darker patches on my arms. This happens with or without sunscreen.

Picture helps. But many supplements can cause hyperpigmentation. Also eczema if a little red can then turn brown due to sun exposure. I would see your dermatologist and also recommend you always wear sunscreen. Other considerations include fungal infections can turn dark with sun, but with correct topicals they will clear,