To constrain a blend curve to a curve-on-surface, snap the blend points to the curve-on-surface. The blend point connected to the curve-on-surface has a GEOMETRY constraint.
When aligning a blend curve to a curve-on-surface, select the blend point that is constrained to the curve-on-surface, then click the GEOMETRY button. The Curvature type changes to PARAMETRIC and the blend curve aligns to the curve-on-surface.