Is the order followed in performing the Isha prayer, the Qiyam (night prayer), and the Isha Sunnah (supererogatory prayer) correct, given that I intended to pray Isha behind an Imam who was performing Qiyam, then I completed Isha individually, then I caught up with the Imam for two Rakahs of Qiyam, then I completed what I missed of Qiyam individually, then I prayed the Isha Sunnah?

It is permissible for a Muslim to pray 'Isha' behind an Imam who is leading Tarawih prayers, according to the Shafi'i school and those who agree with them. This is also the view preferred by Sheikh Al-Uthaymeen. The worshipper should join with the intention of praying 'Isha'. When the Imam concludes the prayer, the worshipper then completes the remaining part of the 'Isha' prayer individually.

As for the Sunnah (definition) prayer of 'Isha', it is preferable to pray it after 'Isha' and before Tarawih. However, if it is prayed after Tarawih or during it, it is still valid. Hanbali jurists have explicitly stated that it is disliked to perform supererogatory prayers between the raka'ahs of Tarawih (the Tarweehah) because it gives the impression of reluctance towards the Imam. Therefore, it is preferable to delay the Sunnah prayer until after Tarawih for this reason, unless there is a prolonged separation, such as the Imam leaving the mosque or a portion of Tarawih being delayed until late at night.