The Prophet's companions did not take as a starting date for the Muslim calendar, the day, the Prophet ﷺ had been sent as an Apostle or the day of his death, but the day of his arrival at Medina.
مَا عَدُّوا مِنْ مَبْعَثِ النَّبِيِّ ﷺ وَلاَ مِنْ وَفَاتِهِ مَا عَدُّوا إِلاَّ مِنْ مَقْدَمِهِ الْمَدِينَةَ
[Machine] "People made a mistake in counting, not in his allegiance or his death, but rather in counting from the beginning of the city."
«أَخْطَأَ النَّاسُ فِي الْعَدَدِ مَا عَدُّوا مِنْ بَيْعَتِهِ وَلَا مِنْ وَفَاتِهِ إِنَّمَا عَدُّوا مِنْ مَقْدَمِهِ الْمَدِينَةَ»
[Machine] The people have not encountered any harm in terms of the number that they counted from the time of the Prophet's ﷺ mission, nor from his death. They have only encountered harm from the beginning of the city.
«مَا أَصَابَ النَّاسُ الْعَدَدَ مَا عَدُّوا مِنْ مَبْعَثِ رَسُولِ اللهِ ﷺ وَلَا مِنْ وَفَاتِهِ وَلَا عَدُّوا إِلَّا مِنْ مَقْدِمِهِ الْمَدِينَةَ»