Decomposition of **3D** structuring elements for morphological operations
I guess this depends on the digital distance transform that one is approximating on the 3d grid and there are various local connectivities possible. There is an implementation in ImageJ here. 

It would also be good to verify if you are using a non-flat structuring element or a correct 3d structuring element. Read Matlab reference here. In the place of euclidean distance sqrt(x.^2 + y.^2 + z.^2) one could add the Manhattan distance using this. Quick 3d distance here.

For 3d structuring element decomposition one can see. But the 3d decompositions of a convex shapes like sphere into separable 2d lines is non-trivial, certain shapes are easier than others like the cube. One can refer here for efficient algorithms for spheres.