I finally found out how to get it to work. First you need an update to version Byobu 5.85 or later. Here is the corresponding commit with the fix and there is a PPA for Ubuntu.
First, check that the line
source-file $BYOBU_CONFIG_DIR/windows.tmux in
/usr/share/byobu/profiles/tmuxrc is uncommented or it won't work.
As you can see in updated documentation part of the commit you need to chain your commands with semicolons. To take the tmux example from the Arch Wiki and make it work it would look like this:
new -A -s SessionName -n WindowName nano;
neww -n foo/bar top;
splitw -v -p 50 -t 0 top;
selectw -t 1;
selectp -t 0
Don't forget to add
-A to the new/new-session command or Byobu will be unable to reconnect to an existing session.
You should update to a newer version of tmux if you are on 14.04 or an older version than tmux 1.9, to avoid running into this issue: Create new-window with current directory in tmux