I can create a position from the organization side and it displays normally in the person's record but does not display from the org side.
The same behavior holds if I create a second position in the same organization from the person side.
However, I see positions displayed for a Foundation but not a Department. Go figure.
If you want to check it out, look at http://220.127.116.11:8080/vivo-isf – Gates Foundation vs. Development Resources Division