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 بِلَالٌ يُؤَذِّنُ ثُمَّ يُمْهِلُ فَإِذَا رَأَى رَسُولَ اللَّهِ ﷺ قَدْ خَرَجَ فَأَقَامَ الصَّلَاةَ»