Answer by Kamil Maciorowski for TO close Tmux along with terminal (if terminal is closed)

From man 1 tmux:

destroy-unattached [off | on | keep-last | keep-group]

If on, destroy the session after the last client has detached. If off (the default), leave the session orphaned. […]

tmux set-option destroy-unattached on will set the option to on for the current session. If you want tmux always to behave like this, set the global option in your .tmux.conf:

set-option -g destroy-unattached on

and restart your tmux server.