  We consider the dynamics of a Bose-Einstein condensate with two internal
states, coupled through a coherent drive. We focus on a specific quench
protocol, in which the sign of the coupling field is suddenly changed. At a
mean-field level, the system is transferred from a minimum to a maximum of the
coupling energy and can remain dynamically stable, in spite of the development
of negative- frequency modes. In the presence of a non-zero detuning between
the two states, the "charge" and "spin" modes couple, giving rise to an
unstable avoided crossing. This phenomenon is generic to systems with two
dispersing modes away from equilibrium and constitutes an example of
class-$I_o$ non-equilibrium pattern formation in quantum systems.
