Hi nos - so that shrinking effect is happening because that one plane surface is a trimmed surface. The underlying surface is actually a fair bit larger than just the trim curves, and the way that Rhino's FlowAlongSrf command works, it just uses the underlying surface directly and doesn't pay any attention to how it is trimmed.

To see the underlying surface, in MoI select that surface and then turn on control points and zoom out a bit and you will see the 4 corner control points for it.

Because the base surface is actually fairly large, that then makes the result in your target surface to be small since the object being morphed is actually small in comparison to the base underlying surface.

There is some description of what an "underlying surface" and trim curves are here:
http://moi3d.com/wiki/FAQ#Q:_Why_does_show_points_work_for_some_objects_but_not_others.3F

So to fix it, select that surface and run ShrinkTrimmedSrf on it, either in MoI or in Rhino. In MoI you need to press the Tab key and type in the command name, or set up a keyboard shortcut for it, it is one of the commands that does not have a button for it in the UI yet.

Running ShrinkTrimmedSrf will shrink the underlying surface down to the trim curves so that it will be the same size as the trim curves and should behave more like you were expecting.

- Michael