What we call "jambiya" is just a short curved dagger traditionally attributed to the "Arab" tradition.
Question: Did it originate in the Arabian Peninsula and spread through the Maghreb, Persia, Middle East etc. with the Arab conquest in the 8th century and beyond or was it originally a local weapon of one of the conquered cultures and adopted by the Arabs? There are many examples of similar daggers in ancient, pre-Islamic, Asian and Scythian cultures (see Gorelik)
No doubt, Arab traders subsequently brought it to Indonesia and beyond. Each culture had its own style, but they often intermixed: one can see, for example, a "typical" Omani one made in India (early globalization!
). Some survived in isolated pockets: Palestinian one (shibriya) or Moroccan Koummya come to mind. Also, there is not much difference between "jambiya" and "'khanjar". Elgood says that it is just a matter of geography: West of the Arabian Peninsula it is Jambiya, East of it it is called Khanjar.
Weapons migrated with the speed of conquering armies and trade caravans.