In this paper, we study totally umbilical $r$-null submanifolds, with $r\ge1$, of a semi-Riemannian manifold using new objects called generalized Newton transformations. We prove that the results presented here are umbrella of the well-known results for totally umbilical null hypersurfaces, totally umbilical half-null submanifolds and generally, totally umbilical $r$-null submanifolds.