Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said:
It is not narrated that the Sahaabah (may Allaah be pleased with them) recited the Talbiyah in unison. Rather Anas ibn Maalik said: We were with the Prophet (peace and blessings of Allaah be upon him) – meaning during the Farewell Pilgrimage – and among us were some who recited “Allaahu akbar”, some who recited “Laa ilaaha ill-Allaah”, and some who recited the Talbiyah. This is what is prescribed for the Muslims: for each person to recite the Talbiyah by himself, and not to pay attention to what others are reciting.
And Allaah knows best.