Collective effects are central in physics, underlying phenomena ranging from phase transitions and pattern formation to synchronization and optimization strategies. Such collective ordering in many-body systems is typically governed by a single order-disorder transition. In driven systems coupled to thermal baths, however, this scenario fundamentally changes; the conventional transition splits into two distinct non-equilibrium critical points. Each reflects a different emergent collective state, and only one such state can function as a heat engine. We demonstrate the robustness of this phenomenon by extending the idealized case of simultaneous bath coupling to a finite-time coupling protocol. We introduce two protocols in which the system interacts with a single bath at a time: a {stochastic} protocol, where the system randomly switches between the baths at different temperatures, and a {deterministic} protocol where the coupling alternates periodically. Our analysis reveals two key results: (i) the splitting of phase transitions persists across all coupling schemes—simultaneous, stochastic, and deterministic—and (ii) different optimizations of power and efficiency in a collectively operating heat engine reveal that both the stochastic and deterministic protocols exhibit superior global performance at finite switching rates and periods when compared to simultaneous coupling. The global trade-off between power and efficiency is described by an expression solely depending on the temperatures of thermal reservoirs as the efficiency approaches to the ideal limit.