Manufacturing new soft materials with specific optical, mechanical and magnetic properties is a significant challenge. Assembling and manipulating colloidal particles at fluid interfaces is a promising way to make such materials. We use lattice-Boltzmann simulations to investigate the response of magnetic ellipsoidal particles adsorbed at liquid-liquid interfaces to external magnetic fields. We provide further evidence for the first-order orientation phase transition predicted by Bresme and Faraudo [Journal of Physics: Condensed Matter, 2007, 19, 375110]. We show that capillary interface deformations around the ellipsoidal particle significantly affect the tilt-angle of the particle for a given dipole-field strength, altering the properties of the orientation transition. We propose scaling laws governing this transition, and suggest how to use these deformations to facilitate particle assembly at fluid-fluid interfaces.