Hi,
It looks like you need to modify the UVs on the surface. Instead of an Unwrap, try a normal UVW modifier in Cylinder projection mode. Update the surface in FP and the branches should follow the flow of the surface.
You will find that the branch density increases at the top where the shape gets narrower, but you can counter this by using the Altitude Density falloff controls found in the surfaces rollout.
I hope that helps
Paul