The imam asks others to lead the people in Taraweeh, then he leads them in praying Witr, then they lead more prayers

Praise be to Allah.

Firstly:

The fact that your friends pray eight rak‘ahs, then the imam prays Witr with three rak‘ahs, makes their prayer complete. So whoever wants to attain the reward of qiyaam al-layl – which the Prophet (blessings and peace of Allah be upon him) promised to whoever prays qiyaam with the imam until he finishes – must pray Witr with the regular imam.

Shaykh al-‘Uthaymeen (may Allah have mercy on him) said:

If there are two imams in one mosque, is each one of them regarded to be independent of the other, or is each one of them a deputy of the other?

What appears to be the case is the latter, that each one of them is a deputy of the other and complementary to him. Based on that, if two imams pray in the mosque, then these two imams are to be regarded as being like one imam, and you should stay until the second imam finishes, because we know that the second one is completing the prayer of the first. End quote.

Majmoo‘ Fataawa ash-Shaykh al-‘Uthaymeen (14/207)

Based on that, the fact that these imams (your friends) step away when the imam prays Witr, means that they are deprived of the reward of qiyaam al-layl.

Secondly:

The fact that your friends come back to lead the people in more rak‘ahs than the imam prayed – whether they come back straight away or after a while – does not deprive those who finished with the imam of the reward of qiyaam al-layl, because the imam’s leading of the people in prayer ended with his Witr.

If someone comes back to the mosque to offer more prayers, those prayers of his are not a completion of the first prayers; rather it is a separate prayer and is not regarded as part of praying with the imam.

For more information, please see the answer to question no. 93907

Thirdly: 

If anyone wants to attain the reward of qiyaam al-layl, then he prays with these people after the imam has finished praying Witr, he should pray Witr with the imam, then after that he may offer as many prayers as he wants, but he should not pray Witr again. Or he may pray Witr with the imam, then when the imam says the tasleem, he should stand up and pray an extra rak‘ah, then he can pray Witr with those people at the end of the night. Both options are permissible. The scholars of the Standing Committee for Issuing Fatwas said: 

If you pray Taraweeh with the imam, then it is best to pray Witr with him, so that you may attain the reward in full, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever prays qiyaam with the imam until he finishes, there will be written for him the reward of spending the entire night in qiyaam.” Narrated by Abu Dawood and at-Tirmidhi. 

If you get up at the end of the night and you want to pray, then pray as much as you wish, without praying Witr, because there should not be two Witrs in one night, as mentioned above. End quote. 

Shaykh ‘Abd al-‘Azeez ibn Baaz, Shaykh ‘Abd ar-Razzaaq ‘Afeefi, Shaykh ‘Abdullah ibn Ghadyaan, Shaykh Saalih al-Fawzaan, Shaykh ‘Abd al-‘Azeez Aal ash-Shaykh, Shaykh Bakr Abu Zayd 

Fataawa al-Lajnah ad-Daa’imah, vol. 2 (6/54) 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said: 

The words “If he follows his imam, he should make it even-numbered by adding a rak‘ah” mean: If the one who wants to continue praying at night follows his imam and prays Witr with him, he should complete it and make it even-numbered by adding a rak‘ah to it. This is the other way for the one who wants to continue praying at night: he can follow his imam in praying Witr and make it even-numbered by adding a rak‘ah, so that the last of his prayers at night will be Witr.

So he may follow the imam, then when the imam says the tasleem at the end of his Witr, he should stand up and pray another rak‘ah, then say the tasleem. Thus he will have prayed two rak‘ahs and that is not Witr. Then if he offers more prayers at the end of the night, he could pray Witr at the end of that. Thus he will attain the virtue of following the imam until he finishes, and he will also attain the virtue of making the last of his prayers at night Witr, which is a good deed. 

… 

If someone were to say: Isn’t this contrary to the words of the Prophet (blessings and peace of Allah be upon him), “Whoever prays qiyaam with the imam until he finishes, there will be written for him the reward of spending the entire night in qiyaam”?                        

Our response is: It is not contrary to it, because the Prophet (blessings and peace of Allah be upon him) did not say: Whoever stands with the imam and finishes praying with him, there will be written for him the reward of spending that night in prayer; rather the hadith defines qiyaam as staying with the imam  until he finishes. So whoever adds anything after his imam has said the tasleem has indeed prayed qiyaam with him until he finished. End quote. 

Ash-Sharh al-Mumti‘ ‘ala Zaad al-Mustaqni‘ (4/65, 66) 

Shaykh Saalih al-Fawzaan (may Allah preserve him) said: 

If a person prays Taraweeh and prays Witr with the imam, then gets up in the night and prays tahajjud, there is nothing wrong with that, but he should not repeat Witr; rather the Witr that he prayed with the imam is sufficient. He may pray tahajjud with the imam as much as Allah enables him to. And if he delays Witr until the end of his prayers at night, there is nothing wrong with that, but he will miss out on following the imam, and it is best to follow the imam and pray Witr with him, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever prays qiyaam with the imam until he finishes, there will be written for him the reward of spending the entire night in qiyaam.” Narrated by at-Tirmidhi (806), Abu Dawood (1375), an-Nasaa’i (1605) and Ibn Maajah (1327). So he should follow the imam and pray Witr with him, and that should not prevent him from getting up at the end of the night and praying tahajjud. End quote. 

Majmoo‘ Fataawa ash-Shaykh Saalih al-Fawzaan (1/435) 

And Allah knows best.