The running node red at start instructions say
Linux users that have a Debian flavour (e.g. Ubuntu, Mint, Debian, etc) are recommended to use the Adding Autostart capability using SystemD instructions from the Raspberry Pi docs though you will need to edit the downloaded /lib/systemd/system/nodered.service file to suit your user id and environment.
So yes you need to follow the pi instructions, especially the bit where it tells you the commands to type. BUT you must also edit the file mentioned above... I.E. change the user from "pi" to whatever your user on Ubuntu is called. This is also documented in the paragraph below the adding autostart section.
