Praise be to Allah.
The view of the majority of scholars is that the traveler is allowed to pray the travel prayer (i.e., shortened) once he has passed the city limits, because the Prophet (peace and blessings of Allaah be upon him) used not to shorten his prayers when traveling until he had left Madeenah. Then he would pray two rak’ahs, because what matters is the time when the action is done. If the muezzin gives the adhaan for Zuhr or ‘Asr, and the traveler sets out and passes the city limits, then he is allowed to shorten the four-rak’ah prayer. What counts is the time when the action is done, not the time when he left the city, because at the time when he does the action he is traveling.