A bit of both but plenty of the latter. My knowledge is when China had Yang, Wu and Jiao provinces rather than when they first up there but during a time where the south was changed from a place of exile those escaping trouble into a power.

As people fled south, for refuge from trouble or floods, for an opportunity of a new life, to escape the heavy obligations and grip of the Han and the landlords, they would consider themselves Chinese if perhaps not always overly keen on being under control from those of the Central Plain, coming to the easy to farm lands of the south or to create new farmland in areas that hadn't been touched before. Of course, there were often locals inconveniently already living there and as the Han expanded its administrative control in the region and inter-marriage happened, more of them got brought under the Han Chinese umbrella. In 2 CE the Han had just two million Chinese there but with migration and agricultural expansion, it was over seven million by the 140s.

More energetic "benvolant" administrators would begin a program of education, pushing Chinese customs and traditions as well as agricultural techniques onto the locals, trying to (not very successfully) curb local beliefs in spirits, divination and local customs, including marriage customs under local religious leaders, that had continued from the days of Chu.

Those who would not accept what was happening could and did rebel and face Han military force to preserve their homes and way of life or be driven out of the valleys and plains into the hills and forests which were less easy to cultivate. The south saw plenty of religious revolts during the days of the Han, though the Han's ability to draw upon resources from across the south or even the empire using the rivers and roads would win over the long term in such clashes. However, those who remained in the valleys worked to keep their beliefs alive to some success, some local beliefs were stamped out but the region's belief in spirits and the mystical arts did not die.

When the Han collapsed into civil war, the Sun family would build upon the platform left behind. The regional pride would end bloodily with a massacre of the northern families but also meant a region not so willing to submit to the northern powers, they were used to gathering around local leaders for self-defence and protection. The population growth that was supplemented by more refugees fleeing the chaos and by raids meant a stable base that could hold on beyond the Yangtze was there, relying (fatally long term) on the support of the major Han-Chinese families of the region. Sun Ce did not like the mystical bent of the region but his younger brother Quan, replacing Ce on his assassination, would embrace it, build a city in Jianye with the wealth and trade of the south as a symbol of southern splendour.

Meanwhile, the Sun forces had a long-running campaign southwards, driving Han Chinese influence south fighting the local Shanyue people in their hills, or refugees from the fighting and small Chinese colonies, taking the lands, resources and people with the flamboyant general He Qi alone supposedly adding tens of thousands to Wu's population and the armies. In areas where keeping hold of the lands might be tricky, the population would be seized and taken further into Wu's grip.

I would recommend the first and fifth chapter of Generals of the South (sadly site is currently down but keeping checking) by Rafe De Crespigny which goes into China's expansion in the south