In general, Islam was spreaded in southeast Asia by trade.
Explanation:
The Silk Road had been, for over two millennia, the chief networking route for all prominent trade throughout Eurasia. It linked various different regions across the two continents with different religions and trades.
This route then became a channel of spreading not only trade and commerce, but also of religion, new ideas and cultures throughout the various regions the road touched which crossing the two continents. The spread of various religions therefore was inevitable.
