The matter is broad in scope and a person may stand up at the beginning of the iqaamah or in the middle of it or after it finishes. The majority of scholars are of the view that if the imam is in the mosque, they should not stand up until the iqaamah ends.
Imam Maalik (may Allaah have mercy on him) said in al-Muwatta’: With regard to people standing up when the iqaamah for prayer is given, I have not heard anything definitive concerning that, but I think it depends on what the people are able to do, because there are heavy and light ones among them and they are not all able to stand up at the same time. End quote.
Al-Haafiz said in al-Fath: The majority are of the view that if the imam is with them in the mosque, they should not stand up until the iqaamah ends. It was narrated that Anas used to stand up when the muezzin said “Qad qaamat il-salaah (prayer is about to begin)”; narrated by Ibn al-Mundhir and others. It was also narrated by Sa’eed ibn Mansoor via Abu Ishaaq that the companions of ‘Abd-Allaah (i.e., Ibn Mas’ood, may Allaah be pleased with him) also did that. It was narrated that Sa’eed ibn al-Musayyib said: When the muezzin says “Allaahu akbar” one must stand up. When he says “Hayya ‘ala al-‘salaah (come to prayer), the rows should be straightened, and when he says “Laa ilaaha ill-Allaah” the imam should say takbeer (to start the prayer). But if the imam is not in the mosque, the majority are of the view that they should not stand up until they see him. End quote.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: Is there any mention in the Sunnah of a specific point in the iqaamah when people should stand up for the prayer?
He replied: There is no mention in the Sunnah of a specific point in the iqaamah when people should stand up for the prayer, but the Prophet (peace and blessings of Allaah be upon him) said: “Do not stand up until you see me.” Agreed upon. If a person stands up at the beginning of the iqaamah or during it or when it ends, all of that is permissible. End quote from Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen (13/16).
And Allaah knows best.