Depends on the Bash version, I guess? Mine is 4.4.20(1) and when I do "cd $HOME/my[TAB]", it replaces the input line with "cd /home/joker/my\ dir/", and pressing [ENTER] changes the directory to '/home/joker/my dir', as can be seen from the prompt.
And I experience the problematic behavior on my Ubuntu VM. However, I can get the above describe expansion behavior if I run: shopt -s direxpand