Sounds like you created this user with the `useradd` command. This is a low level command, and not the prefered way to create a user. By default it will point the user's shell to /bin/sh, not /bin/bash. So you will not get the nice autocompletion. You can use the `chsh` command to change the user's shell:
sudo -u $USERNAME chsh -s /bin/bash
This should give you bash autocompletion. You probably also want to copy /etc/skel/.bashrc to the user's home directory.
In the future, prefer the `adduser` command. Despite the similar name, it has different results. It will default to using /bin/bash as the shell and seed the new user's home directory with the files from /etc/skel/