We explain an elementary, topological construction of the Springer representation on the homology of (topological) Springer fibers of types C and D in the case of nilpotent endomorphisms with two Jordan blocks. The Weyl group action and the component group action admit a diagrammatic description in terms of cup diagrams appearing in the context of Khovanov arc algebras of types B and D. We determine the decomposition of the representations into irreducibles and relate our construction to classical Springer theory. In addition to that we give a presentation of the cohomology ring of the two-block Springer fibers in types C and D.