[tjoff]

tmux keeps the selection to the pane for me.

Not something I make use of though, feels faster to copy using the keyboard instead.

[xhrpost]

Did you have to use a particular setting? I looked into it a few times but couldn't figure it out.

[tjoff]

Tried it in a container with only "set -g mouse on" in the config and it works fine (v. 3.2a).

My best guess is that your terminal selection is overriding tmux.