The presence of a large inverse magnetocaloric effect around the martensitic transformation in Ni-Mn-Sn and Ni-Mn-In alloys is expected to lead to substantial cooling on applying a magnetic field. However, the occurrence of hysteresis around the transition causes limitations on adiabatic temperature-changes. We study the adiabatic temperature-change in both systems in relation to the hysteresis effects. Ni-Mn-In, having a relatively narrower hysteresis and a greater shift of the characteristic transition temperatures with applied field with respect to Ni-Mn-Sn, shows reversibility in the adiabatic-temperature change related to the inverse magnetocaloric effect when the state of the system is cycled within a minor transitional hysteresis loop. Ni-Mn-Sn does not show reversibility in the inverse magnetocaloric effect under cycling-fields up to 5 T. The reversibility in the adiabatic temperature-change is directly related to the reversibility in the relative amount of austenite and martensite in the sample when the field is cycled.