Earlier quoted context omitted.
You're right about who is causing the damage etc. but the 'commons' does not refer to the people; it refers to the shared resource. So a public park is the commons. And when it gets polluted with plastic rubbish etc. because externalities are not internalized that's a tragedy of the commons.
The fallacy in "the tragedy of the commons" is that there's something inherent in having a shared resource that dooms the shared resource. At least this is the popular understanding. And I'll add that if we look at shared resources both with more breadth -- e.g. across history and cultures -- and in more depth -- e.g. cross-analysis, they come out looking much more successful than you'd think.
It is about the idea that when there is a limited, shared public resource, individuals making rational self-interested decisions will often lead to a situation which no individual would choose.
That doesn’t mean it always has to end in tragedy, though. It just means you can’t just go fully “laissez faire” and let everyone do whatever they want, and expect the common to be preserved. The only way to protect the common is to take some sort of collective action; pass a law that limits how much an individual can take from the common, or set a quota and allow people to bid, etc.
The collective action doesn’t even always have to be a legislative action; you could create a taboo around using too much of a common, or use social shaming to get people to only use their share.
The point is that you have to take SOME collective action to prevent the tragedy.