Hello,
I have to thank you for your question, I enjoyed doing the tutorial myself.
After three attempts to get the problem you have, I could not.
[EDIT] Yes I see the problem! I wasn't looking at the correct side, but now as I look at the far side I see the extra diagonal lines. Hm... not sure if the other times I did it those were there...,
SO:
What I did is,
get a jpeg of the vase in plan view from the internet
drew a straight segmented poly-line,
used the pet palette to curve each line into the proper curve,
created the morph surface - raised it into a volume, and
pushed an offset down to form the thin walls.
At this point I should have seen your problem, I did not -
I assume that your issue must come from the line work you based
the morph from. Did you use splines or the magic wand to trace a imported shape?
At any rate try it with the polyline like I did, see if that works.