If a worshiper unintentionally sat for the Tashahhud twice, in the second and third rak'ahs, does this necessitate prostration of forgetfulness (sujud al-sahw) if he remembered in the fourth rak'ah and completed the prayer?

Your completion of the prayer after remembering the addition, and your performance of the prostration of forgetfulness (sujud al-sahw), were correct. This is because you inadvertently added something to your prayer that was of its own kind. Your ruling is to perform two prostrations of forgetfulness after the salām (greeting of peace that concludes the prayer) as an expiation for the forgetfulness. This applies if you were an imam or praying alone. However, if you were a follower (ma'mum), then there is no prostration upon you, as the imam bears that responsibility.