Latin is quite a strange language. It never really died, or it did die but with a slow and uneven death. The example you being is emblematic: as the international language of scholars in Europe, when the new word "Musa" gets adopted in the 18th century from the arabic "mauz", on one hand sure, it's technically Latin and thus yes technically there is a Latin word whose etymology traces back to an Austronesian root.

I'm the other hand though it clearly doesn't mean that this happened during ancient Roman times, which is the conclusion one would easily jump to under the assumption that Latin really died long long ago.

Lingua latina mortua est, vivat lingua latina!

Yes most probably through trade. Check the provided video link on the ancient Pompeii, based on the archeological evidences they had trading activities with other Asian countries including India. It is already known that the Chams already settled in Vietnam during Pompeii time. Their ports popularity at the time probably similar to Singapore today and Singapore is currently the busiest port in the world. Another fun fact is that the Chams ancient capital city is called Simhapura or Lion City, and Singapore original name is Singapura. My gut feeling is that Champa was either playing the role of Singapore today or conquered Singapore, at the time of Pompeii.