If you want to record your fancy tmux session with all windows and splits recorded you can do it in the following way:

• setup your tmux session (tmux new [-s session-name], create windows, splits, start processes in them)
• detach (prefix+d)
• run asciinema rec --command "tmux attach [-t session-name]" tmux-$(date +%F--%H%M).cast
• when you're finished, just detach the session again

If you're already inside of tmux, you can detach+reattach in one command: tmux detach -E 'asciinema rec -c "<tmux attach or tmux new>" tmux.cast'

Consider wrapping it in a shell function (bash/zsh compatible):

tmux-rec() {
    local date=$(date +%F_%H%M)
    local cmd=(asciinema rec -c "tmux new -s recording-$date" tmux-$date.cast)

    if [[ -v TMUX ]]; then tmux detach -E "$(printf '%q ' "${cmd[@]}")"; else "${cmd[@]}"; fi
}