Not at all, really. Korea was anywhere between a third to a half completely annexed by the Han, Wei, and Western Jin Dynasties. The rest of the Korean peninsula were direct tributary clients. That's about as far as China ever got to actually controlling Korea, but there were several later attempts which may or may not succeed depending on the scenario. At this same time Shi Xie of the Later Han, and later Wu consolidated much of northern Vietnam into China (where it would remain until the Song Dynasty was conquered). The Han Dynasty had a rather extensive empire in Central Asia, but this was largely martial and beyond a few military colonies nothing was done to colonize the region. The Tang went a little further, perhaps having recognized authority to the Caspian with a powerful military force that occupied a role similar to that of a Central Steppe Khan until An Lushan crippled the Tang and the balance of power shifted to the Arab allied Turks. Lastly, Taiwan was subject to at least three invasions that we know of that all failed do to disease and cost. Eastern Wu of the 3rd Century briefly conquered the island, but withdrew after a couple years with major casualties. The native populous was reported to have been similar to the old Yue and Wu state some fifteen hundred years prior to that point, but this is highly contested as a historical reality. The Sui made an invasion of either Taiwan or the Philippines around the time they invaded Korea, and whatever good fortune the expedition may have had it was expensive, had a number of diseases and plagues, and was ended prematurely do to the Korea disaster.
There were attempts, and limited success, on all these fronts. The issue is that they never really materialized. China's internal problems ended Central Asian supremacy, China's conquest by the Mongols led to Vietnam's permanent departure, China's best opportunity to take over Korea was dashed by a mixture of Chinese instability, foreign invasions, and the deposition of the clan that had successfully conquered the peninsula, and the other opportunities were long shots as they occurred, while Taiwan's largest problem appears to be disease and the weather - which means the people were largely being taken from parts of China other than Fujian and nearby provinces.
Depending on the PODs and the directions of the butterflies, its really not impossible to see one or two of them becoming success stories. Its certainly a lot harder, but it is possible for all avenues to work.