You're right, it isn't. Its complicated.
During the early Imperial period (200s BC-600 AD): at the heart of the tributary system is the idea that the Chinese Emperor- the Huangdi- is a world ruler. As per the Meandate of Heaven beliefs that the Heavens accorded to the Virtuous Huangdi rule of the world. The problem with that is no matter what the Chinks believed, the Huangdi did not rule other people's states, no matter how powerful he is.
So here's the problem: how the hell can the Huangdi claim to rule "All under Heaven" if other people don't exactly obey him?
Ultimately, ancient Chinese diplomacy solved this Sinocentric conundrum by coming up with the 冊封 Cèfēng system, which is what westerners translate as "Tributary System." In the Cefeng system, all the world was seen as subjects of the Chinese Emperor. His main subjects - the people he actually rules- are called the "inner subjects," those under Chinese hegemony (i.e. subjugated steppenigger/jungle tribes, and sometimes Korea and Vietnam) were called "Outer Subjects" while the "Barbarians" of the world are simply just furthest from the Son of Heaven's light.
As such, Barbarians were simply viewed as future vassals of the Chinese Emperor. So whenever they meet Barbarians, the Chinese always try to impress their civilization's superiority over barbarians in an attempt to convince them of their vassalhood, and once the barbarians "accept" this, they can begin normal trade relations, in which China for the longest time always had the upper hand in.