Whenever Ibn Umar entered the outer boundary of the Haram, he would stop reciting the talbiyah. He would then spend the night at Dhu Tuwa, pray the morning prayer there, and perform a ritual bath. He used to relate that the Prophet of Allah ﷺ used to do the same.
كان ابن عمر، إذا دخل أدنى الحرم أمسك عن التلبية، ثم يبيت بذي طوى، ثم يصلي به الصبح ويغتسل ويحدث أن نبي الله ﷺ كان يفعل ذلك.
Bukhari related it in the Hajj chapter (1573) via Ismail bin Ulaya, and Muslim related it in the Hajj chapter (1259) via Hammad bin Zayd, both of them from Ayub, from Nafi, with this wording. The wording given here is Bukhari's. The hadith of Ismail bin Ulaya, from Ayub, from Nafi, from Ibn Umar, was related by Ahmad (4628) with a longer account, and this is his wording.When Ibn Umar entered the nearest part of the sacred territory, he would stop reciting the talbiyah. When he reached Dhu Tuwa, he would spend the night there until morning, then pray the dawn prayer, perform ghusl, and relate that the Messenger of Allah used to do this. Then he would enter Makkah in the forenoon, go to the House, touch the Black Stone, and say, "In the name of Allah, and Allah is greatest." Then he would jog around three circuits, walking the two remaining stretches. Whenever he came to the Black Stone he would touch it and say "Allah is greatest," completing four circuits while walking. Then he would go to the Station and pray two units of prayer, then return to the Black Stone and touch it. Then he would go out to Safa through the main gate, stand upon it, and say "Allah is greatest" seven times, three times each occasion, and after each set of three he would say, "There is no god but Allah alone, with no partner, His is the dominion and His is the praise, and He has power over all things." End of the hadith.His statement "seven times" means he would stand on Safa seven times, saying "Allah is greatest" three times on each occasion.As for Tirmidhi's statement, after relating the hadith via Abdul-Rahman bin Zayd bin Aslam, from his father, from Ibn Umar, who said, "The Prophet performed ghusl for his entry into Makkah at the conquest," Tirmidhi said, "This hadith is not preserved. The sahih version is what Nafi related from Ibn Umar, that he used to perform ghusl for entering Makkah." He also said, "Abdul-Rahman bin Zayd bin Aslam is daif in hadith. Ahmad bin Hanbal, Ali bin Madini, and others have declared him daif, and we do not know this hadith as a raised report except through his narration." End of quote.This requires scrutiny, because it is established in the Sahihayn as a raised report from the hadith of Ibn Umar. The apparent meaning of the statement that the Prophet used to do this refers to everything mentioned before it, including the ghusl.