The transformation of normal vectors differs from the transformation of position vectors.

\[\V{v}'=\M{M}\cdot\V{v}\] \[\V{n}'=(\M{M}^{-1})^T\cdot\V{n}\]If a vertex position is transformed by $\M{M}$ then the vertex normal must be transformed by $(\M{M}^{-1})^T$.

A normal vector describes an *orientation* instead of a position. It defines a plane equation (a row vector) and encompasses an infinite set of points that fall on that plane. Details here.