When the Republic of China retreated to Taiwan they did not have to file for asylum or apply for a Visa. Taiwan was part of China. The Communist Party is declaring when they won the civil war they gained control over all of China, including Taiwan.
This is the narrative for Taiwan not having sovereignty, and not necessary my own views.
Another way to look at it is if the Confederacy never surrendered to the union and instead retreated to Cuba and became the dominant political force on that island.
So this analogy might work better if Confederacy was the one who won, and Union retreated to Cuba.
Today, Cuba happens to be a highly desirable location (strategically, or for resources, or etc.). So Confederates, who now control continental U.S., want to maintain their claim on it.
Meanwhile, nowadays a majority of the people in USA (a government which controls only Cuba) consider themselves Cubans, and almost no one in USA cares about regaining control of continental U.S.
But Confederates feel that, if USA renounces control of continental U.S., it would be a step towards USA independence, which would further weaken Confederate claim over Cuba. So they pressure USA to keep referring to themselves as "USA" instead of "Cuba". Additionally, they think that the "one America" stance depends to some extent on USA retaining continental U.S. in its official borders. (But in reality, no USA citizens, aka Cubans, care about these borders continuing to include continental U.S.)
I almost feel like control of Taiwan is more a matter of national pride for the PRC than geopolitics at this point. Yes, the PRC would love to get the USA out of the South China Sea, but there are already American forces in Japan that aren't leaving anytime soon. Yes, the PRC would love to add Taiwan to its territory, but it should be mostly happy enough just to continue building economic ties. However, both the government and the people see possession of Taiwan as unfinished business and this is what I think drives their dramatic reactions in cases like this Apple incident, which is what I was trying to illustrate with the analogy.