  We investigate how the breaking of charge conjugation symmetry $\mathcal{C}$
impacts on the dynamics of a half-filled fermionic lattice system after global
quenches. We show that, when the initial state is insulating and the
$\mathcal{C}$-symmetry is broken non-locally by a constant magnetic flux, local
observables and correlations behave as if the symmetry were unbroken for a time
interval proportional to the system size $L$. In particular, the local particle
density of a quenched dimerized insulator remains pinned to $1/2$ in each
lattice site for an extensively long time, while it starts to significantly
fluctuate only afterwards. Due to its qualitative resemblance to the sudden
arrival of rapidly rising ocean waves, we dub this phenomenon the ``tsunami
effect". Notably, it occurs even though the chiral symmetry is dynamically
broken right after the quench. Furthermore, we identify a way to quantify the
amount of symmetry breaking in the quantum state, showing that in insulators
perturbed by a flux it is exponentially suppressed as a function of the system
size, while it is only algebraically suppressed in metals and in insulators
with locally broken $\mathcal{C}$-symmetry. The robustness of the tsunami
effect to weak disorder and interactions is demonstrated, and possible
experimental realizations are proposed.
