Considering this proposal is used for the key exchange, they definitely need to update both the client side and server side part to be able to make use of it. That’s the kind of thing that may take years but luckily it can fall back to older methods.
It also needs to be thoroughly vetted so that’s why it’s a hybrid approach. If the quantum resistant algorithm turns out to have problems (like some others have), they’re still protected by the traditional part like they would have been, with no leaking of all the data.