Martensitic and magnetic properties of ferromagnetic shape memory alloys are known to depend up on structural modulations and associated changes in the Fermi surface. These modulations although periodic and spanning over multiple unit cells, involve movement of atoms typically of the order of 0.01Å. Therefore X-ray Absorption Fine Structure (XAFS) is an ideal tool to map both, local atomic movements and changes in density of states (DOS) due to changing hybridization as the system transforms from austenitic to martensitic phase. This paper presents a compilation of our XAFS studies on the Ni-Mn based shape memory alloys. A complete description of the changes in local structure around the constituent metal ions in the following alloy compositions: Ni2+xMn1-xGa, Ni2Mn1.4Sn0.6 and Ni2Mn1.4In0.6 in the austenitic and martensitic phases have been obtained. The results give the new experimental evidence for the crucial hybridization component that influences and leads to structural transition in these Ni-Mn based Heusler alloys.