I would say the West has been doing this for the last 200 years. The U.S learned from the British, and the British ruled half of the world back then.Its super hard to do this. This requires an elaborate structure and most importantly experience. The US has a well oiled coup machine as they've been practicing this for over a century & is a critical part of their foreign policy.
China is new in this and is still in learning phases. But for this to happen, China has to employ dirty tactics. Like for example what if this group you talk about tries to fleece China of its money or double cross you? What will China do about it? Stop the money? Thats it?
How many overseas assassinations has China carried out? Can China eliminate a foreign politician for double crossing them? CIA sure does and that's how they keep their assets in check. US has hundreds of mercenary groups across the world to carry out such acts, how many does China have?.
Money alone doesn't work, there needs to be an element of coercion alongside. The latter is lacking in Chinas Foreign Policy .