During the time of the spice trade which took place in the Indian ocean, many of the traders were arab (muslim). Over time many of the rulers in southeast asia wanted a stronger conection with these traders. Thus many of them converted to islam. Over time the people, who wanted to follow the king converted as well.

Southeast asia is special as compered to the rest of the muslim world because islam came through trade not conquest.

Note: I am not a Ph.d historian so feel free to say were I am wrong