Was Tayma' part of the Arabian Peninsula at the time of the expulsion of the Jews?

Question:
And was Tayma' outside the Peninsula when 'Umar expelled them to Tayma'?

Answer:
It appears that it was attached to Sham, and these are part of the Kingdom, Tayma' and Tabuk. However, the apparent meaning of their expulsion to Tayma' is that it was attached to Sham at that time, and it was within the borders of Sham at that time, after it had been conquered. As for now, it is part of the Peninsula.
The student: The commentator said: "They are two extended areas, and they are two well-known villages. In this is evidence that the Prophet (peace and blessings be upon him) intended by expelling the Jews and Christians from the Arabian Peninsula their expulsion from part of it, which is the Hijaz specifically; because Tayma' is from the Arabian Peninsula, but it is not from the Hijaz."
The Shaykh: No, the correct view is the entire Peninsula; the Hijaz is part of it. Yes.
Q: But is Khaybar part of the Peninsula?
The Shaykh: Yes, Khaybar is from the heart of the Peninsula. And from the Hijaz.
Q: How do we reconcile this with the Prophet's command to expel them from the Arabian Peninsula?
The Shaykh: 'Umar expelled them after that.
The student: Qadi 'Iyad mentioned, saying: "And Arajah and Tayma' are two villages in Sham?"
The Shaykh: According to his independent legal reasoning.