Source: Fatawa Muhammadiyah, Vol. 1, Page 320
❀ Question
When should the Iqamah (Takbeer) be called?
❀ Answer
الحمد لله، والصلاة والسلام علىٰ رسول الله، أما بعد!
The answer to this question has already been provided in the response to Question No. 2.
Jabir bin Samurah (RA) narrates that Bilal (RA), after giving the Adhan, would wait for a while. When he saw the Messenger of Allah (ﷺ) coming out, he would then begin the Iqamah.
ھذا ما عندي والله أعلم بالصواب