Global quenching of quantum many-body models can induce periodic dynamic quantum phase transitions (DQPT) directly connected to zeros of the Landau order parameter (OP). It has been argued that the relevant dynamics closely resemble the Rabi oscillations characteristic of two-level systems. Here we address the question of whether this DQPT behavior merely exhibits the limits of an effective two-level system, or whether it can occur as part of more complex dynamics. We focus on quantum many-body scarring as a useful toy model that naturally allows us to study state transitions in chaotic systems. DQPT shows the change in the dominant contribution to the wavefunction of the degenerate initial state manifold, and the direct relation to the OP zero is in the special case of occurring at the midpoint of the uniformly degenerate manifold can be seen to occur only. Our work generalizes previous results and reveals that, in general, periodic DQPTs are composed of complex many-body dynamics that radically exceed those of two-level systems.