Answer: That depends on which type of magic they are using. In the case of soul-based inherent magic, no, the plane of residence has no real effect barring possible psychosomatic ones ("I'm on the Plane of Fire, I can't summon water because I believe I can't"). Natural magic on the other hand is always dependent on the plane and hence the nature of the current plane affects its manipulation. Also, all natural types of magic vary from each other and it takes some time to attune to a new plane in the case of a caster who uses natural magic.