What likely happened was mostly cultural diffusion and the spread of Islam through trade and cultural intercourse, much like it's spread throughout Sub-Saharan Africa. Muslim traders ventured far and wide across South-East Asia, with Malacca being a huge center of trade between India and China.

Many rulers of small trading kingdoms along the way converted, and with them their subjects often converted as well, either because of the political and economic advantages of sharing a religion with many of the most powerful traders, or due to a particularly pious and convincing trader. While it's hard to say specifically why some spots converted and others did not, the consensus is that this was a largely peaceful process that spread due to the strong trade links Southeast Asia had with the Muslim world.

In terms of further reading, M.N. Pearson, The Indian Ocean (Seas in History), Routledge, 2003. is an excellent resource for further study.