Harsh Siberia and even harsher Cossacks
When we talk about Siberia, first thing we notice is that this huge area is very sparsely populated, both today and in history. This is not without the reason. Climate in Siberia is harsh, with relatively short summers and long, cold winters. As a result, classical agriculture with grain is almost impossible. Thus, it is very hard to create classical village settlements - there is simply not enough food for usual farming population and fodder for the cattle .
As a result, Siberia was largely inhabited by nomads, with occasional market towns which were only permanent settlements. Primary economical products of such a way of life were cattle in large herds and fur from hunting. Nomads would occasionally organize themselves into conquering hordes and raid their more sedentary neighbors to the East and West (China and Russia) . But, in the end, nomads could not create great civilizations. With the advent of technology (especially firearms) they were beaten back to their steppes and forests. Now it was the time for counter-attack.
As mentioned before, Siberia didn't have much to offer economically, and main thing that interested early explorers and conquerors like Yermak Timofeyevich was fur. Fur was much in the demand (winter and ceremonial clothes for nobility), was relatively portable and had large price/weight ratio. Cossacks , as and odd assortment of free people, robbers, explorers, daredevils and brigands, were naturally drawn to this potentially large profit. Of course, fur and ore traders like Stroganovs sensed opportunity as well. They tactically encouraged and financed Cossack expeditions deep into Siberia, promoted exploration of river routes and took over old Siberian Tatar settlements and forts, also building completely new. Latter, they started trade in bulkier goods like ore and timber, although this largely depended on waterways and latter railway. Somewhat latter, Russian Imperial government started their own colonization of Siberia, by moving mostly convicts into large territory. Even when finished with their sentence they could not return to Russia. Instead they remained in Siberia. As a rule, they would depend on food and other things imported from mainland, therefore there were no serious attempts of rebellion, to separate and form independent state.
Now, it is a well known fact that Cossacks and other Russian explorers went all the way to Pacific, and to Chinese, Mongolian and Korean border. Chinese and Koreans had occasional border clashes with them that are well documented. Question remains, why Chinese didn't attempt to explore on their own deeper into Siberia ? Most likely answer is that they didn't have a class of free vagabonds like Cossacks. Yes, there were bandits in China, sometimes even warlords. But, they didn't have support of central authorities, or some special status. They were either criminals, or if they became powerful enough robber barons. Prevailing ideology in China was Confucianism, with the stated goal of preserving and harmonizing existing status between Heaven and Earth. Much was written about Chinese isolationism in those years, and this is no place to search for causes. It is sufficient to say that China effectively stifled foreign trade, especially private trade. Considering that they need anything from surrounding "barbarians" , they didn't feel the need to expand. And unlike Russia, they didn't permit private initiative in exploring. As a consequence, even in 16th and 17th century it was the Russians (Cossacks) that traveled all the way to China, not the other way around.