It seems more like the majority of borosilicate vials are produced outside of China. It doesn't even look like China has any significant domestic production capacity for the type of high quality chemically inert glass needed for vaccine vials, that's why the tubes for production are mostly imported.

Main producers of vials seem to be SCHOTT, Stevanato Group, Gerresheimer, Corning, and DWK Life Sciences, from Germany, Italy and the US.

SCHOTT alone is looking to increase production until the end of 2021 by about seven billion vials [1], which would be 3.5 times more in additional production output than the complete annual production capacity of Zhengchuan Pharmaceutical, which according to the article is one of China's largest producers.

[1] https://www.pharmtech.com/view/readying-glass-vials-for-vacc...

It also says there are 60 other companies working in China.

> China has some 60 glass medicine container providers

Plus we’ve seen markets adapting really quickly already a ton of times through out the pandemic.