A detailed study on quaternary ordered full Heusler alloys CuNiMnAl and CuNiMnSn at ambient and under different compressions is presented using first principles electronic structure calculations. Both the compounds are found to possess ferromagnetic nature at ambient with magnetic moment of Mn being 3.14 μB and 3.35 μB respectively in CuNiMnAl and CuNiMnSn. The total magnetic moment for both the compounds is found to decrease under compression. Fermi surface (FS) topology change is observed in both compounds under pressure at V/V0 = 0.90, further leading to Electronic Topological Transitions (ETTs) and is evidenced by the anomalies visualized in density of states and elastic constants under compression.