You should look at Greg Friedman's book:
http://faculty.tcu.edu/gfriedman/IHbook.pdf
CS-sets are discussed in section 2.3. In fact for many purposes it is rather interesting to suppose that the links $L$ are just compact filtered topological spaces and not CS-set. 
The definition does not imply $L$ is itself a CS-set. 

Such an inductive assumption is useful when you want to study pseudomanifolds and Poincaré duality of pseudomanifolds in intersection homology.