The onset of abrupt magnetic reconnection events, observed in the nonlinear evolution of double tearing modes (DTM), is investigated via reduced resistive magnetohydrodynamic simulations. We have identified the critical threshold for the parameters characterizing the linear DTM stability leading to the bifurcation to the explosive dynamics. A new type of secondary instability is discovered that is excited once the magnetic islands on each rational surface reach a critical structure characterized here by the width and the angle rating their triangularization. This new instability is an island structure-driven nonlinear instability, identified as the trigger of the subsequent nonlinear dynamics which couples flow and flux perturbations. This instability only weakly depends on resistivity.