Ni-Mn-based Heusler alloys, in particular all-d-metal Ni(-Co)-Mn-Ti, are highly promising materials for energy-efficient solid-state refrigeration as large multicaloric effects can be achieved across their magnetostructural martensitic transformation. However, no comprehensive study on the crucially important transition entropy change Δs_t exists so far for Ni(-Co)-Mn-Ti. Here, we present a systematic study analyzing the composition and temperature dependence of Δs_t. Our results reveal a substantial structural entropy change contribution of approximately 65 J(kgK)^-1, which is compensated at lower temperatures by an increasingly negative entropy change associated with the magnetic subsystem. This leads to compensation temperatures T_comp of 75 K and 300 K in Ni₃₅Co₁₅Mn_50-yTi_y and Ni₃₃Co₁₇Mn_50-yTi_y, respectively, below which the martensitic transformations are arrested. In addition, we simultaneously measured the responses of the magnetic, structural and electronic subsystems to the temperature- and field-induced martensitic transformation near T_comp, showing an abnormal increase of hysteresis and consequently dissipation energy at cryogenic temperatures. Simultaneous measurements of magnetization and adiabatic temperature change ΔT_ad in pulsed magnetic fields reveal a change in sign of ΔT_ad and a substantial positive and irreversible ΔT_ad up to 15 K at 15 K as a consequence of increased dissipation losses and decreased heat capacity. Most importantly, this phenomenon is universal, it applies to any first-order material with non-negligible hysteresis and any stimulus, effectively limiting the utilization of their caloric effects for gas liquefaction at cryogenic temperatures.