I've wondered the same thing. It seems unpredictable.
For example, in a Spin synth where it does not consist of a full orbit (the loop does not close) the default seems to make the starting photo the center of the arc - and this applies to the thumbnail on the profile page as well, I believe.
Usually on a partial Spin, I would prefer to make the first photo taken the beginning point, so I edit that manually and it seems that on some of the video thumbnails, it updates to reflect the new starting photo and in others it does not.
At a recent concert, I shot some partial spins of the stage. Some began from stage left and some from stage right, but of course the defaut starting view was center for them all, as far as I can recall.
Here are the links to the thumbnails:
http://photosynth.net/preview/users/Nathanael#11 (thumbnail now starts from right)
http://photosynth.net/preview/users/Nathanael#10 (thumbnail still starts from center)