These Chinese police patrol around tourist areas with local police. You don't go to a consulate when you lose your mobile phone or someone steals your wallet.
These are police who operate in concert with local police. The whole point is to help Chinese tourists I think. It's not for anything nefarious...It's too racist to be smearing everything Chinese under the banner of the current Western-'China-bogeyman'-hysteria
I personally think it is outrageous that the US government (or state or local governments) allows China to station police officers on US soil, and gives them the right to act in a police capacity. I am not ok with that at all, even if what you suggest as their purpose is correct.
Why would this even be necessary, if they're here for the purpose you suggest? Local police can handle these sorts of cases, and cities where tourists tend to travel certainly have translators on staff. Hell, cities in the US have translators to help with residents whose English skills are poor.
Also: it's not "racist" to dislike this sort of thing if the foreign government in question is not aligned values-wise with your own. I don't think it's remotely appropriate for an authoritarian anti-democratic country to have law enforcement influence on our soil.
I wouldn't have the same reaction if, say, a tight US ally (South Korea or Japan, to pick examples from the same part of the world) were to have an informal police presence in the US. But even then, I would expect them to be working with the FBI (or similar) on higher-level international crime matters (sorta like an Interpol type thing), not working on local crime. Foreign police forces should not have any kind of jurisdiction in "local" crimes.
If Chinese want to do covert action overseas they don't send police to do it I think... It would not be covert.
This mushing together is like a racist smear fear mongering. It's bad.