Magnetic refrigeration working based on the magnetocaloric effect can be the perfect replacement of the conventional gas compression-based refrigeration technology and reduces its harmful effects on the environment. The boundary between a first-order and a second-order phase transition would be where the perfect magnetocaloric material would be found. Therefore, establishing the sequence of phase transitions clearly is essential for the characterization of other phase change materials and for applied magnetocaloric research. A quantitative fingerprint of second-order thermomagnetic phase transitions is reported here in Si-substituted high content Mn-based inverse Heusler alloy systems, which are found to be crystallized in cubic structures. The second-order nature of the phase transition has been confirmed from the Arrott plot analysis and a correlation between magnetocaloric effect and local exponent is established. Using the Arrott plot, the critical exponents are evaluated employing different techniques such as modified Arrott plot, Kouvel–Fisher method, and critical isotherm. Their values are found to be in great agreement with each other and follow the mean-field model signifying the presence of long-range ordering in the materials. The high value of isothermal magnetic entropy change and the reversibility justifies the suitability of the reported materials in the practical application as magnetic refrigerants.