In our part of the world, I have noticed a few people standing up for the salah when the caller pronounces the words “Haiya as Salah” during the iqamat and most stand up from the beginning of the iqamat. Which is correct?
There is no specific evidence on the right time to stand up once the iqamah starts, and this is what Ibn Uthaymeen says. The various schools have used different arguments to justify different times for standing up. But since there is no strong evidence on any of these opinions, you are free to stand whenever it suits you. There is a hadith in Sahih al-Bukhari in which the Prophet says not to stand up until the crowd sees him stand up, therefore if there is a specific person who is meant to lead the prayer, then the rest should wait for that person to stand up before standing up themselves.
The Hanafi opinion is to stand up when the athan reaches “hayya alas salat”.
The Shafiee opinino is to stand up once the athan is finished.
The Maliki opinion is that you can stand any time, at the beginning, middle or end of it.
The Hanbali opinion is to follow what the imam does. The imam is supposed to stand up once the athan reaches “qad qamatis salat”. But if the imam takes longer to stand up, then the rest will wait until the imam stands up.
However, if there is a specific imam who is meant to lead the prayer, and the imam is late, and the iqama is said, the rest should wait for the imam to arrive before standing up.