I am currently reading Livy's "Early History of Rome" and am up to the part during the reign of the Tarquins, right after the death of Servius, where he is talking about the ascendant Roman supremacy over the Latins and refers to consulting with the "asian communities"
Who would he have been referring to at that time?
Do you have a direct quote with paragraph numbers?
In 1.45 of Livy's History of Rome, tangentially meantions the Temple Diana at Ephasus -- which is located in what is today the Ionian Coast of Asia Minor.
My understanding is that that time "Asia" meant what we now call "Asia Minor" which roughly corresponds to the Modern nation of Turkey. At that time, the area was controlled by Greek-speaking people organized into a mix of Kingdoms and semi-autonomous city-states.
The farthest East the Romans had direct contact that has good evidence is the Middle East in today's words. They had a different word to refer to China, the few times a mention is made, whether it be diplomatic or trade. Pliny the Elder mentions the Seres here, http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0137%3Abook%3D34%3Achapter%3D41 .