During my undergrad university days (at the University of Utah), I took some Mandarin classes. There was a local Confucius Institute which provided various free materials in Chinese to the campus library. The extent of my direct contact with them was receiving a couple hundred dollars for doing well in a Mandarin speech contest they held for my class.

It was obvious that there was a certain propaganda aspect to this outreach effort; the reading materials provided of course didn't go into any potential negatives of the Beijing government, etc. Very much in line with the CCTV news network. My Mandarin teacher was Taiwanese and so I think that was good for me in that I wasn't getting all my exposure to Chinese from a single source.

I would not be surprised at all to learn that Chinese government operatives were using these various state-funded educational agencies for gaining intelligence and promoting their ideology. I assume the US is doing the same thing. It's a long game, with assets being put into place sometimes decades in advance. A healthy dose of cynicism is always important when dealing with state-funded groups; it's rare that countries invest such resources just out of the goodness of their altruistic hearts.