Like Charles said the white tape edging encircles the entire blue cross. The Staunton and Charleston Depot (among others) flags had no edging on the ends of their blue crosses. In Heraldry (Coat of Arms) which flags evolved from it was not permitted in principle to place color on color without a border or fimbriation to separate between the two. This allowed the colors to be better seen from a distance. What is interesting the official flag specs of May 1, 1863 did not call for the blue cross to be completely edged with a white fimbriation, yet the Richmond Depot did it's own thing.
Here is an example of a Richmond Depot 2nd National flag: