We discuss the progress on exactly solvable multistate Landau-Zener models from the perspective of their application to competing reactions of particle creation from a false vacuum. Such models generally predict that, even with identical initial conditions and nearly the same other particle parameters, quantum coherent evolution results in a final particle distribution with significant asymmetry. We use an exact solution of the driven bosonic Tavis-Cummings model for two reaction pathways to quantify this effect, reveal a corresponding phase transition, and identify its universality class. These studies of quantum phase transitions can be relevant to quantum optics, condensed matter physics, quantum simulations, as well as cosmology and high-energy physics.