Nonadiabatic excited-state molecular dynamics (NEXMD) has been used to study photodecomposition in a class of recently synthesized bicyclic conjugated energetic materials (CEMs) composed of fused tetrazole and tetrazine derivatives with increasing oxygen substitutions. Modification by oxygen functionalization has already been demonstrated to increase the two-photon absorption intensity in the target CEMs while simultaneously improving oxygen balance. Photodecomposition mechanisms in materials that undergo nonlinear absorption could be used to achieve controlled, direct optical initiation. Here, we use NEXMD simulations to model the nonradiative relaxation and photodecomposition in CEMs following photoexcitation by a simulated Nd:YAG laser pulse. Excess electronic energy is quickly converted into vibrational energy on a sub-100 fs time scale resulting in bond dissociation. We find that, for the studied tetrazine derivatives, the bicyclic framework is an important structural feature that enhances the photochemical quantum yield and the high atomic oxygen content increases the relaxation lifetime and opens additional photodissociation pathways targeting the oxygen-substituted sites. The presented analysis scheme based on bond orders in the swarm of NEXMD trajectories is a useful tool for determining photochemical reactions.