  In most lattice models, the closing of a band gap typically occurs at
high-symmetry points in the Brillouin zone. Differently, in the Creutz model
$-$ describing a system of spinless fermions hopping on a two-leg ladder
pierced by a magnetic field $-$ the gap closing at the quantum phase transition
between the two topologically nontrivial phases of the model can be moved by
tuning the hopping amplitudes. We take advantage of this property to examine
the nonequilibrium dynamics of the model after a sudden quench of the magnetic
flux through the plaquettes of the ladder. For a quench to one of the
equilibrium quantum critical points we find that the revival period of the
Loschmidt echo $-$ measuring the overlap between initial and time-evolved
states $-$ is controlled by the gap closing zero-energy modes. In particular,
and contrary to expectations, the revival period of the Loschmidt echo for a
finite ladder does not scale linearly with size but exhibits jumps determined
by the presence or absence of zero-energy modes. We further investigate the
conditions for the appearance of dynamical quantum phase transitions in the
model and find that, for a quench {\em to} an equilibrium critical point, such
transitions occur only for ladders of sizes which host zero-energy modes.
Exploiting concepts from quantum thermodynamics, we show that the average work
and the irreversible work per lattice site exhibit a weak dependence on the
size of the system after a quench {\em across} an equilibrium critical point,
suggesting that quenching into a different phase induces effective correlations
among the particles.
