[Machine] The Prophet's muezzin would call for prayer, then wait. And when he saw the Prophet approaching, he would start reciting the adhan.
«كَانَ مُؤَذِّنُ النَّبِيِّ ﷺ يُؤَذِّنُ ثُمَّ يُمْهِلُ فَإِذَا رَأَى النَّبِيَّ ﷺ قَدْ أَقْبَلْ أَخَذَ فِي الْإِقَامَةِ»
Bilal would call the Adhan, then he used come to wait. When he would see that the prophet ﷺ had come out (of his house), he would pronounce the iqama.
كَانَ بِلاَلٌ يُؤَذِّنُ ثُمَّ يُمْهِلُ فَإِذَا رَأَى النَّبِيَّ ﷺ قَدْ خَرَجَ أَقَامَ الصَّلاَةَ
Bilal would call the Adhan, then he used come to wait. When he would see that the prophet ﷺ had come out (of his house), he would pronounce the iqama. (Using translation from Abū Dāʾūd 537)
كَانَ مُؤَذِّنُ النَّبِيِّ ﷺ يُؤَذِّنُ ثُمَّ لَا يُقِيمُ يُمْهِلُ حَتَّى إِذَا رَأَى النَّبِيَّ ﷺ قَدْ خَرَجَ أَقَامَ الصَّلَاةَ