All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Imam Muslim reported that Ibn ‘Abbaas said: “The people (pilgrims) used to leave Makkah in every other direction (and haphazardly). Thereupon, the Prophet said: “Let none of you leave Makkah before making Tawaaf around the Ka'bah, as the last of Hajj rites.”
Based upon this Hadeeth Muslim scholars agree that one should leave Makkah right after performing the Farewell Tawaaf. Staying for a short time does not have any effect on the Tawaaf; therefore, the mentioned situation is considered as a slight delay, which does not influence Tawaaf.
Allah knows best.