According to Darrell Wolcott, a well-known historian of ancient Welsh history ( see his Welsh history museum in Texas ) Eochaid, the youngest of his siblings, came to Dyfed around 343 as part of a deal negotiated with the Romans whereby the Deisi would receive the protection of the Roman empire from their enemies in Ireland and in return would populate a thinly settled area of West Wales as a deterrent to further Irish invasions (see later). The family thereby became accustomed to the culture of Romano-British culture and way of life. As a result, he and his descendents, through marriage or power, became the ruling Kings of Dyfed.

Here I see parallels to Greek history where Alexander the Great, 600 years earlier, put his cousin Ptolemy on the Egyptian throne who quickly adopted Egyptian culture, and claimed Pharaonic status. His descendant, Cleopatra, later formed an alliance with the major power at the time, the Roman Empire.

This understanding is reflected in what we read on Wikipedia about the kingdom of Dyded. i.e.

The kingdom may have been founded by Irish immigrants, the Deisi, in post-Roman times; its royal dynasty lasted until Llywarch ap Hyfaidd’s death (904), when his daughter’s husband Hywel Dda, son of the king of neighbouring Seisyllwg, succeeded; Dyfed then became part of the larger Deheubarth. Norman raiders arrived from the north-east in 1073–4, and ten years later Pembroke’s fortress was built; thereafter, Dyfed was gradually replaced by several marcher lordships. The memory of Dyfed survived, not least in the Welsh prose tales, the Mabinogi, which were published in English translation in the 19th cent.