I prayed Ishā’ behind the Imām leading the Tarāwīḥ prayer, and after the taslīm, I completed four more rakahs with him. Is my prayer valid?

Praise be to Allah, and prayers and peace be upon the Messenger of Allah, and upon his family and companions.

Your prayer is valid, but it is better to complete it alone. It is permissible to pray 'Isha behind Tarawih, and after the Imam says the salām, the worshipper completes his remaining two rak'ahs. If the latecomer sits after the Imam's salām in the position of the first tashahhud, his prayer is valid, though disliked. However, if he is not in the position of tashahhud and sits intentionally, his prayer is invalidated. If he sits forgetfully, his prayer is valid with the prostration of forgetfulness (sujud as-sahw).