Hard to say without actually seeing the car. But if it's pretty mild swirling that only appears in certain lighting conditions, oftentimes a 2-step system (if Meguiars) is enough to get rid of them. Oh yeah, make sure that the detailer doesn't glaze over the swirls instead of removing them completely.
it really depends on what condition of the paint, light swirl marks can be removed by using a 3M machine glaze with foam pad. Then for added protection apply 3M show car paste wax. For heavy swirl marks better use 3M perfectitII rubbing compound w buffing pad, den machine galze and wax.