It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) heard a man saying the talbiyah on behalf of someone else, so he asked: "Have you said the talbiyah on your own behalf?" He said: No. So he said: "First say the talbiyah on your own behalf, then say it on behalf of someone else."
It has also been narrated from Ata from Aishah (may Allah be pleased with her), and from Ata from the Prophet (peace and blessings be upon him) as mursal; the first narration is the more correct, and Allah knows best.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 8679