Your Copy Lands in Two Places

The same sheet in two boxes; only one is open
The same sheet in two boxes; only one is open

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.