He was riding behind the Prophet ﷺ from Muzdalifah and continued reciting the talbiyah until he threw the pebbles at the Jamrah.
حدثنا عباد بن عباد عن ابن جريج عن عطاء عن ابن عباس
أنه كان ردف النبي ﷺ من جمع فلم يزل يلبي حتى رمى الجمرة
Its chain of transmission is sahih. Abbad bin Abbad bin Habib bin Muhallab bin Abu Sufra Azdi was reliable, one of the teachers of Ahmad. Qutayba counted him among the noble jurists, Malik, Layth, Abdul-Wahhab Thaqafi, and Abbad. He was a sensible, cultured man, and Ahmad's statement will come later, after hearing a hadith from him, he said, "I began to marvel at Abbad's eloquence." The hadith was narrated by the authors of the six books, as found in Dhakhair Mawarith 6068, and see what follows at 1805.