No, your act is wrong.

You should pray with the Imam until he concludes all his 23 rak’ah. If he prays the last 3 rak’ah like Maghrib prayer, pray with him but when you offers salam, you should stand up and finish your 4th rak’ah. Later on, you can offer witr in your home or in the masjid.

And Allah knows best

In our country imam dose not recites tahjud prayers in congregation.how many rakahs are there in tahjud.in our country imam normally recites 20 rakahs but i normally quit after 10 rakahs and then i perform 1 rakah of witr indiviually because they perform witr in a way which is not in accordance with the saying of the prophet(peace be upon him).is my act correct?