It is shown that the presence of particles of the γ-phase in NiFeGaCo single crystals has an influence on the mode of the formation of the martensite phase: while in the homogeneous (free of precipitates) sample the transformation underwent by single interface motion, in samples with precipitates many martensite needles were formed and grown in two specific directions. Similarly the shape and the area of hysteresis curves are also different. These differences are accompanied with differences in the critical exponents of distributions of the energy (determined from both thermal and acoustic noises) and the amplitude (obtained from acoustic emission measurements). In addition the values of these exponents were different for heating and cooling. We found a definite correlation between the relative changes of these exponents and the ratios of the numbers of hits and integrated energies of acoustic emission during heating and cooling: if the later ratios were negative then the changes in the exponents had opposite sign, if the exponent was larger for heating than cooling, then the energy of acoustic emission was smaller for heating than cooling. In homogeneous crystals without γ-phase precipitates positive asymmetry was obtained while in crystals with large γ-phase precipitates (5–15 μm) negative asymmetry was observed. Aged crystals with bimodal structure (large and small γ-phase particles 5–15 μm + 150–300 nm) are between these cases: the relative changes are practically zero.