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The structural and magnetic properties of functional Ni-Mn-Z (Z=Ga, In, Sn) Heusler alloys are studied by first-principles and Monte Carlo methods. The ab initio calculations give a basic understanding of the underlying physics which is associated with the strong competition of ferro- and antiferromagnetic interactions with increasing chemical disorder. The resulting d-electron orbital dependent magnetic ordering is the driving mechanism of magnetostructural instability which is accompanied by a drop of magnetization governing the size of the magnetocaloric effect. The thermodynamic properties are calculated by using the ab initio magnetic exchange coupling constants in finite-temperature Monte Carlo simulations, which are used to accurately reproduce the experimental entropy and adiabatic temperature changes across the magnetostructural transition.