We present new experimental results on the quenching dynamics of an extended thermo-convective system (a network array of approximately 100 convective oscillators) going through a secondary subcritical bifurcation. We characterize a dynamical phase transition through the nature of the domain walls (1D-fronts) that connect the basic multicellular pattern with the new oscillating one. Two different mechanisms of the relaxing dynamics at the threshold are characterized depending on the crossing rate $\mu=\left.\frac{d\varepsilon}{dt}\right|_{\varepsilon=0}$ of the quenched transition. From the analysis of fronts, we show that these mechanisms follow different correlation length scales $\xi \sim \mu^{-\sigma}$. Below a critical value $\mu_c$, a slow response dynamics yields a spatiotemporal coherent front with weak coupling between oscillators. Above $\mu_c$, for rapid quenches, defects are trapped at the front with a strong coupling between oscillators, similarly to the Kibble-Zurek mechanism in quenched phase transitions. These defects, pinned to the fronts, yield a strong decay of the correlation length.