Hi Brian, yeah that's right, in addition to the rotation and u/v mirroring the mapping of surface normal to surface normal can also come into play. That one does not have any effect in several cases though like if you are flowing curves that are only right on the surface, or objects that stick halfway out on both sides of the surface. But if stuff pokes out just to one side then if the default normals does not do what you want the "Flip surface normal" checkbox can be used to correct that one.

Hmmm, now that I read your post more carefully I see that you're getting slightly different behavior with the "rigid" option enabled, that happens with your text because the rigid option takes the bounding box around each individual object and basically only flows the center point of that box from the base to the target, then does a move + rotate of the object to align the base position with the target position. With your text, the bounding box of each object is a little different, that's why you will see those results. The rigid option would have more uniform behavior when you have some array of a bunch of duplicated objects and you're trying to put that pattern onto a shape without any distortion.

- Michael