The first time tmux starts when @continuum-boot is set to 'on' tmux-continuum will generate a user level systemd unit file which it will save to ${HOME}/.config/systemd/user/tmux.service and enable it. From then on when that user logs in, either through a GUI session or on the console or via ssh, Systemd will start the tmux server.
The command used to start the tmux server is determined via the @continuum-systemd-start-cmd option that can be set in .tmux.conf. (Remember to reload your configuration with tmux source ~/.tmux.conf afterwards.
The default command to use is new-session -d. If you want more control over what sessions get started then you should set up your sessions in tmux.conf and set @continuum-systemd-start-cmd = 'start-server'. As this will be executed as part of systemd's ExecStart statement there will be no shell parsing. See Systemd manual for more details.
To control the tmux service you can use all the standard systemctl commands using the --user argument. eg to see if the tmux server has started:
systemctl --user status tmux.service