Typically the way these kinds of missile emplacements work is that first the ships are spotted with a command/radar unit, which then tries to categorise the ships based on their radar "signature" - in this case signature is literal, in the sense that each class of ship and sometimes even within classes has a unique radar reflaction that can be detected. Most major millitaries over the years of shadowing each other have built up databases of each other's craft including radar signatures from every angle. This is then used to prioritise targets and decide on an attack profile - so it's unlikely it would accidentally be launched at say a destroyer. They then send this plan to their missiles which all start their attack independantly, using their onboard radars to follow the target. The usual countermeasures to this like I mentioned involve using chaff, which is little bits of metal foil that are launched into a cloud in the sky, which presents as a big cloud on the enemies radar behind which the missiles cannot see. This is where manouvering may be used, if the missile momentarily cannot see then you may be able to avoid it. However with swarm attacks, which is how these missiles will almost certainly be deployed at least against a target as valuble as a carrier, they come from several directions which makes deploying chaff and/or manouvering very difficult.

I don't claim it's some secret that only china has or anything like that - the US and several other countries have deployed them as well. Its just that the vulnerability of carrier groups to them necessitates a shift in naval strategy closer to "fleet in being" - essentially that capital ships are too valuble to risk losing so are restricted in where they can operate because they are more valuble as a deterrrent than they would be actually fighting - which reduces power projection ability of carriers, similar to what the early 20th century did to battleships