The rovibronic spectrum of the Na-3 B system is computed taking into account fulI rovibronic coupling between different vibronic states. The rovibronic coupling matrix elements are calculated using the vibronic states following from a pseudo Jahn-Teller model for the vibronic dynamics in the B system. Comparison with results of optical-optical double resonance measurements [W. E. Ernst and S. Rakowsky, Can. J. Phys, 72, 1307 (1994)] shows good agreement. In particular, certain properties of the Coriolis splittings, so far explained by an ad hoc spin-rotation interaction, are now well understood as the consequence of rovibronic coupling between two vibronic states, A general discussion of rovibronic dynamics on electronic potential energy surfaces with three equivalent minima is presented.