I'm glad you specified Tang and Northern Song, since different dynasties have different methods of assimilating conquered territories. I'm quite weak with regards to the history of the Song Dynasty, so I'll tackle the Tang Dynasty exclusively. Specifically, I can shed some insight on Tang China's policy regarding conquered Central Asian territories.

As you may know, the Tang Dynasty under Emperor Taizong conquered large tracts of land in Central Asia from the nomadic steppe tribes that were native to the region. However, Emperor Taizong didn't treat all the conquered peoples the same way. His two most significant methods were resettlement and puppet states.

Let's start with the resettlement strategy. Specifically, the resettlement of the Eastern Tujue, or the Eastern Turkic Khanate. At the time, they were the Tang Dynasty's northernmost neighbor, and border conflicts as well as uneasiness with having steppe nomads in such close proximity to the Tang Dynasty's northernmost provinces led the Tang Dynasty to launch a successful invasion of the Eastern Tujue. After the Eastern Tujue's lands were conquered, Emperor Taizong asked for suggestions from his closest advisors as to how to deal with them. One of the more popular suggestions to Emperor Taizong at the time was to force the conquered nomads to sinicize by moving them to powerful and predominantly Han Chinese provinces like Shandong, and scatter them throughout the prefectures within the province to make it hard for them to reorganize.

However, an advisor named Wen Dalin persuaded Emperor Taizong otherwise, convincing him to resettle these nomadic tribespeople within the Tang Dynasty's northernmost and mostly uninhabited prefectures. In doing so, these conquered tribes retained their tribal customs, helped to populate unsettled land, and were given vassal ranks. Han Chinese who were enslaved by the Eastern Tujue were ransomed back rather than simply reclaimed/rescued. In exchange for all this, the newly vassalized Eastern Tujue were required to provide a levy of their cavalry to supplement Tang military forces whenever Taizong wished it. This was somewhat similar to the Roman Empire's policy of recruiting 'barbarian' soldiers from conquered regions to fill specialty roles.

Next, let's talk about the puppet state strategy. In particular, the conquest of the Xianbei-inhabited state of Tuyuhun, Tang's western neighbor at the time. The Tang invasion begun as a result of the Tuyuhun's ruler, Murong Fuyun, disrespecting and antagonizing Emperor Taizong. The Tang campaign's successes, and the subsequent defeat of the Xianbei forces, then led to Murong Fuyun being killed by his own soldiers out of resentment for him being the trigger to the conflict. Because the campaign started due to Murong Fuyun's transgressions, the Tang goal was to punish Murong Fuyun rather than conquer the region. So when Murong Fuyun's son, Murong Shun, submitted to Tang rule, he was made the new ruler of Tuyuhun by the Tang forces - albeit one that was a vassal of the Tang Dynasty.

The puppet state strategy tended not to work out too well (for the Xianbei at least), however, and required constant 'maintenance' so as to speak. Murong Shun's subservience unfortunately led the Xianbei to rebel against his rule, and he was assassinated. Murong Shun's son, Murong Nuohebo, succeeded Murong Shun, but there was massive civil unrest among the Xianbei and Murong Nuohebo could not consolidate control. In response, the Tang forces again attacked the Xianbei again to make them accept Murong Nuohebo's rule. This would have been the end of the matter... only now that civil unrest was dealt with, outside powers came into play in the form of the Tibetans. Unable to withstand the Tibetans started attacking Tuyuhun, Morong Nuohebo uprooted his people, sought refuge with his Tang overlods, and ultimately the Xianbei ended up resettled in China anyway.

There's more, but Emperor Taizong's campaigns were numerous and to address all of them in detail would derail from your original question. TL;DR, Imperial China, at least during the Tang Dynasty, relied on resettlement and puppet states as two of their main methods of dealing with conquered territories in Central Asia.

Source: Bo Yang (1987), "Outlines of the History of the Chinese" or "中國人史綱"