The microscopic theory of field-induced spin-mixing instabilities in antiferromagnetic molecular wheels CsFe8 is proposed. The basic features of magnetic torque measurements [O. Waldmann, Phys. Rev. Lett. 96, 027206 (2006)] are well explained by the interplay of three basic ingredients: the spin-mixing vibronic interaction with field-dependent vibronic constants, cooperative elastic interactions, and spin-mixing interactions independent from vibrations. The main contribution to spin mixing comes from second-order zero-field splitting mechanisms. At variance with previous interpretations, we find that the observed anomalies are not associated with a phase transition.