Yes, once your stack reaches the edge of their highlighted move spaces, their turn is over whether you attacked/used an ability or not. On the flip side, (for most units/abilities) once you attack/use an ability, their turn is over whether you moved them or not. So you are correct, in order to attack someone (with melee) they would have to be inside of the available move spaces.
You can however move them partially within their max move spaces then 'wait', then finish moving them or use an ability/attack once everyone else has gone for the turn.
Hope that helps --- The most objective point of view is a cynical one.