There's no such thing as "between" turns. You're either on Turn 1 or Turn 2. They might do something where you prepare to cast on Turn 1, and so do nothing else that turn, and can then cast on Turn 2, but not prepare to cast on Turn 1, cast "between" turns and can then do another action on Turn 2 (that would defeat the point of having some spells take a turn to prepare).
