Within the scope of molecular quantum computing with vibrational qubits, we analyse the impact of phases that are present during the quantum computation processes. While the phase relation in superposition states and its temporal evolution are crucial to any implementation of quantum computing, we elucidate the special challenge that emerges for phase control of qubits encoded in molecular vibrational eigenstates. Phase correctly prepared superposition states in general exist only for a finite time and with the inherent entanglement in molecular vibrational qubit systems their development displays a complex pattern. We show that the free relative phase evolution in such qubit systems can be utilized for the implementation of quantum phase gates. Moreover, a practical experimental realization of phase correct quantum gates acting on molecular vibrational qubits could be accomplished by a decomposition into laser-induced population transfer and free evolution phase gates. This concept adds to the flexibility in the implementation of quantum gate sequences and algorithms. A modification, where only a reduced number of selected relative phases needs to be adjusted, will make this scheme more robust and versatile. Finally, we also disclose and discuss another key feature for the implementation of phase correct quantum gates, i.e. the dependence of the quantum gate fidelity on the absolute or carrier-envelope phase of the driving femtosecond laserfield.