What is the prayer time that should be followed in electronic Adhan applications when there is a difference between the Umm Al-Qura time and the Islamic Association of North America time?

When in doubt about the start of prayer time due to differing calendars, one must wait and not pray until there is certainty or strong probability that the time has begun. The prayer is not valid if there is doubt about the start of its time. So, if certainty or strong probability is achieved by the later timing, then one must act according to it, not the earlier calendar.