Your head stays on a point at eye level while the body already turns, then snaps around to find it again. It curbs dizziness and centres the turn.
Whether you fall out of a double pirouette almost never comes down to talent, but to two things: core tension and spotting. It's the same trick figure skaters use to avoid getting dizzy – the head stays on its point as long as possible, then whips around and finds it again instantly. The most common error is looking at the floor: it tips your axis forward and you turn straight into the wobble. The second is a lazy head that drifts round with the body instead of snapping. Drill it standing still first, head only, no body rotation; then shuffle slowly around your own axis while holding the point. Salsa uses the same mechanism, except there the head follows only at the end of the turn. Ballroom Standard does the opposite: you don't spot there, the head simply stays quiet over the spine.