So the only solution to keep enjoying asian music on your Firefox / Mac is to find a website that streams through flash. And I have found one such website!
99.cn is one of the many asian music streaming websites from China. It uses flash, so it will definitely work on any web browser that has Adobe Flash plugin!
Based on my observations, all those streaming websites have the same musc catalogs, if not almost the same.
Go ahead and enjoy your favorite asian music from 99.cn
Note: These music streaming websites from China might not have the proper licenses from artists to broadcast music. Please listen at your own risk.