We study strong field molecular ionization, with a focus on indirect ionization to dissociative excited ionic states. Indirect ionization, also known as post-ionization excitation, refers to the excitation of the molecular cation following ionization to a lower lying state. We propose two possible mechanisms underlying indirect ionization -resonant transitions facilitated by nuclear dynamics and non-adiabatic transitions driven by the laser field off resonance. We compare them by measuring the dependence of the indirect ionization yield on pulse duration for cations with different electronic structures. Both experiments and simulations confirm the importance of nuclear dynamics in indirect ionization and indicate the presence of off-resonant non-adiabatic transitions.