ANSWER:

If the imam prays taraweeh and then concludes it with witr, this means that he has finished his prayers of the night. 

He should not pray witr if he intends to offer tahajjud as this is wrong of him. 

Therefore, praying taraweeh and witr with him is sufficient for you and this would count as praying the whole night in Sha Allah.

QUESTION: Praying night prayer behind the imam = reward of praying whole night. If I prayed taraweeh/witr with the imam after Ishaa, and there is another session of night prayers hours later, do I have to attend both to get this reward?

Taraweeh, Tahajjud and Qiyam-ul-Layl |