The Aksu Huafu Textile Factory was named in video reports issued by a now-detained Uyghur.
Tuo Zhen's promotion is linked to his willingness to purge liberal media outlets under general secretary Xi Jinping.
Critics say the Holy See is selling out to the Chinese Communist Party, where religious persecution continues unabated.
Families are calling for international pressure on China to release the detainees, who include at least two minors and one Portuguese national.
