We combine experiments and theory to investigate the orientational dynamics of dipolar ellipsoids, which self-assemble into elongated ribbon-like structures due to the presence in each particle of a permanent magnetic moment perpendicular to the long axis. Monodisperse hematite ellipsoids are synthesized via sol-gel technique, and arrange into ribbons in presence of static or time-dependent magnetic fields. We find that under an oscillating field, the ribbons reorient perpendicular to the field direction, in contrast with the behaviour observed under a static field. This observation is explained theoretically by treating a chain of interacting ellipsoids as a single particle with an orientational and demagnetizing field energy. The model allows describing the orientational behaviour of the chain and captures well its dynamics at different strengths of the actuating field. The understanding of the complex dynamics and assembly of anisotropic magnetic colloids is a necessary step towards controlling the structure formation which has direct applications in different fluid-based microscale technologies.