Magnetocaloric effect (MCE), magnetization, specific heat, and magnetostriction measurements were performed in both pulsed and steady high magnetic fields to investigate the magnetocaloric properties of Heusler alloys Ni50-xCoxMn31.5Ga18.5 (x = 9 and 9.7). From direct MCE measurements for Ni41Co9Mn31.5Ga18.5 up to 56 T, a steep temperature drop was observed for magnetic-field-induced martensitic transformation (MFIMT), designated as inverse MCE. Remarkably, this inverse MCE is apparent not only with MFIMT, but also in the magnetic-field-induced austenite phase. Specific heat measurements under steady high magnetic fields revealed that the magnetic field variation of the electronic entropy plays a dominant role in the unconventional magnetocaloric properties of these materials. First-principles based calculations performed for Ni41Co9Mn31.5Ga18.5 and Ni45Co5Mn36.7In13.3 revealed that the magnetic-field-induced austenite phase of Ni41Co9Mn31.5Ga18.5 is more unstable than that of Ni45Co5Mn36.7In13.3 and that it is sensitive to slight tetragonal distortion. We conclude that the inverse MCE in the magnetic-field-induced austenite phase is realized by marked change in the electronic entropy through tetragonal distortion induced by the externally applied magnetic field.