If you enter the mīqāt boundary without having the intention to proceed to Makkah for ʿUmrah or Ḥajj, then it is not necessary to assume the iḥrām. Since your destination when landing in Jeddah was Madīnah and not Makkah, there is no need to put on iḥrām from that location, since Madīnah is outside of the mīqāt boundary.

Allah knows best,

Imam Mustafa Umar