In natural hair that is not grey, but is darker like yours is naturally, there are an overload of pigments called melanin. The darker your hair is, the more red and brown tones are jammed into those melanin cells. As you get older, those cells tend to lose their pigments which lead to them going a clear colour. To you it may seem grey.
When you use an artificial colour on your hair from either the salon or the supermarket, the tones your hair naturally lack tend to remain in your hair and when it grows out you might see a reddish brown tone on your grey. This can be eliminated by asking your stylist to use a blue based colour or using a colour that contain blue pigments. Violet shampoos might help to remove some of those tones on a temporary basis. Either way this is a very common problem.