when adding a new tab, the default directory of the new table should be following the current directory, it's very useful, gnome-terminal and roxterm also do like that.
xfce4-terminal does that for me too. Make sure your shell sources /etc/profile.d/vte-2.91.sh on startup.
Yes, xfce4-terminal should be opening new tab with the current active directory by default.
See bug 13902.
If nothing helps, try checking "Run command as login shell".