While I can't speak to the specifics of Hinduism in Southeast Asia specifically, it might be informative to consider how Hindusm spread within South Asia. For what it's worth, there is a general confusion over the caste system among Western audiences, who imagine it to be an consuming obsession in Ancient (and modern) India. In truth, caste was more fluid, and the confusion arises from the conflation of two distinct identity labels - varna and jati.

In Southern India during the Sangam period (~ 500 BCE), home to a thriving Dravidian culture, Hinduism and the Vedic culture tended to spread through Brahmins invited by Kings to settle the land. Generosity to brahmins and their protection was one of the hallmarks of kingship in the Vedic model, and the Sangam Era Kings were keen to be seen as equals of the Kings in the North of India. Crucially, Brahmins were necessary to perform the Vedic rituals. Brahmins were offered land to settle, called agraharas. These brahmins reaffirmed the status of the King and his clan as Kshatriyas, and in turn the King upheld the traditional Kshatriya role of generosity to Brahmins. To establish the vedic credentials of the King, the traditional dieties of the ruling clan were identified as aspects of the Vedic pantheon, bolstering their claim to the Vedic ideals of a righteous King. A prime example of this expansion of Hindu theology was the identification of the Dravidian War God Murugan with the Vedic War God Kartikeya.

It wouldn't be too far off the mark to suggest that early adopters of Hinduism took the Vedic Varnas as a prescriptivist model, and simply overlayed it onto the contemporaneous social heirachy. Ruling clans were identified as Kshatriyas, and the status of brahmins were reaffirmed. Critically, Brahminhood could only be passed down through the family, though they could, and did wives from the local communities.

It would seem reasonable that a version of this process played out in Southeast Asia. Indeed, we have a relatively recent example to compare with - the adoption of Hinduism in the 18th century by the Kingdom of Kangleipak in Northeast India. King Pamheiba adopted Hinduism, and made it the State Religion. The Kingdom took the Sanskrit name of Manipur, and the ruling Meitei tribe were recognized as Kshatriyas.