This feature (content assist) supported in all versions of DBeaver and for all types of databases.
Just tested exactly this query (select * from users u u.) and it works fine.
Do you see table columns after you enter "u." and wait for a second?
May be the problem is in broken shortcut.
If it doesn't work anyway, could you check error log (menu Window -> Error Log) for errors after you press Ctrl+Space?