This is the second part of the work on differential models of the Anderson duals to the stable tangential \( G \)-bordism theories \( I\Omega^G \), motivated by classifications of invertible QFT's. Using the model constructed in the first part [Journal of Gökova Geometry Topology, 16, (2023), 1-64], in this paper we show that pushforwards in generalized differential cohomology theories induces transformations between differential cohomology theories which refine the Anderson duals to multiplicative genera. This gives us a unified understanding of an important class of elements in the Anderson duals with physical origins.