Well... I don't think CIA directly sponsored the Xinjiang terrorism. Unless you can find some sources for that.
Even without the CIA, Xinjiang will have the terrorism separatism problem. Xinjiang is cursed to share a border with Afghanistan. The Afghans were forced into militancy due to Soviet Invasion and CIA sponsored the militancy through Pakistan (Along with the Oil rich Arab countries).
Xinjiang became an issue after Turkic ethnic members of the radicalized jihadist militant group decided that since they more or less crippled Soviet, why not try to do the same with China to achieve independence. Quite logical.
There was definitely foreign incitement and funding of terrorism in Xinjiang by foreign agents, but that was actually more the doing of the Soviets rather than the Americans.
After the Sino-Soviet split, the USSR employed agents to bribe locals to attack Chinese interests in Xinjiang, especially the oil and gas infrastructure.
You have foreign agents popping up with suitcases of money in villages so poor no one there had previously seen a 50 yuan note, and tasked the locals to blow up pipelines, power lines and the like and to attack Chinese construction crews and oil refineries.
More often then not, when they attacked manned outposts, PAP guards and even militia would absolutely slaughter them as they just had primitive hunting rifles or melee weapons against assault rifles. But that only made things worse as suddenly the whole bloody tribe then decided they have a blood feud with the authorities, so generate after generation would go to war and get annihilated and deepen the blood feud.
Source: close family who worked for Sinopec and had decades to first hand experience working in Xinjiang.
All the Islamic extremism BS is just a modern facade over these old historical grievances.
When the Soviets collapsed and Sino-Russian relations improved, obviously the Russians stopped their efforts to destabilise Xinjiang. The hatred they created still remained, but without foreign support could not accomplish much, so they went out looking for new sponcers and found extremist Islamists in Afghanistan. They have been supplying foot soldiers in exchange for training and weapons since.
America did support them for a short spell, but after 9/11, it was too politically toxic to support people who are sometimes literally in bed with Al-Q and the Taliban.