In our previous article (Chion and Tojeiro, Ribaucour Partial Tubes and Hypersurfaces of Enneper Type. Advances in Submanifold theory and related topics, Latin American Mathematical Series, UFSCar Subseries, Springer, 2025), we introduced the concept of a Ribaucour partial tube in a space form and proved that it can be characterized as an immersion of a product of two manifolds such that the distributions given by the tangent spaces of the factors are orthogonal to each other with respect to the induced metric and are invariant under all shape operators, and one of them is spherical. In this article, we prove a de Rham-type theorem that provides conditions under which a certain Riemannian manifold is locally isometric to a product manifold whose metric is conformal to a polar metric and then use the characterization above of Ribaucour partial tubes to derive a general decomposition theorem for immersions of product manifolds which extends various related results.