When does one stand up to make up missed units of prayer?

Only once the imam has completed the greeting of peace to both sides. Until then one is still part of the congregational prayer and follows the imam.

Someone who arrives late for a congregational prayer joins the imam wherever he is in the prayer. The units they have missed are made up alone afterwards. The only question is at what moment they may stand up to do so.

The answer follows from the role of the imam. Whoever prays behind him follows him. Whatever is binding on the imam in that prayer is binding on the follower too. You bow when the imam bows, and you remain seated as long as the imam is seated.

The congregational prayer ends with the greeting of peace, first to the right and then to the left. So the latecomer stays seated until the imam has said the second greeting as well. Only then do they stand up and complete their prayer. Standing up after the first greeting means leaving the imam too early.

Sometimes people make particular movements when standing up, such as a fixed order in which the arms are released or folded. Such habits have grown up in certain places. They are not part of Islam and are not required.

The second hadith above shows the spirit of this rule. You come without hurrying, pray what you can catch with the imam, and calmly complete the rest. In this way the congregational prayer stays orderly, and no one disturbs anyone else.