Your Copy Lands in Two Places

In tmux copy mode, copy with Enter and paste into another pane with ]. All of that stays inside tmux.
The next thing anyone tries is pasting the same text into a browser or a chat window.
What you copied went into a tmux buffer, which is not your system clipboard.
tmux does try to reach the system clipboard too (set-clipboard defaults to external). It uses OSC 52, a signal asking the terminal to write to the clipboard.
Whether it gets out depends on two things: tmux knowing the terminal understands the signal (the Ms entry in terminfo, which tmux adds itself for xterm-like terminals), and the terminal accepting it. Some terminals ignore it; others accept it only once you turn it on in their settings. The signal travels across SSH, so even tmux on a server can write to the clipboard on your desk.
A copy lands in two places. One of them always, the other only if the terminal accepts it.
