That is one meaning of “commons”, but not all of them, and you might be mistaking which one the phrase ‘tragedy of the commons’ is using.

“Commons can also be defined as a social practice of governing a resource not by state or market but by a community of users that self-governs the resource through institutions that it creates.”

https://en.wikipedia.org/wiki/Commons

The actual mechanism by which ownership resolves tragedy of the commons scenarios is by making the resource non-free, by either charging, regulating, or limiting access. The effect still occurs when something is owned but free, and its name is still ‘tragedy of the commons’, even when the resource in question is owned by private interests.