The ramifications of gust-front on atmospheric surface layer turbulence is a vexing issue, with nearly no information available over the Indian region where such events are not uncommon. Over the Indian peninsula, our recent field-experimental study has shown that a cold pool associated with the gust-front creates two distinct regimes in ASL turbulence, where temperature fluctuations display contrasting behavior. In this work, we use a multi-level observational dataset to evaluate the corresponding impacts on the moisture fluctuations and turbulent heat and moisture transport. We discover that the topology of the turbulent structures, which govern the temperature and moisture fluctuations, clearly exhibit a regime-wise distinction. In the first regime, the structures in temperature and moisture fluctuations are inclined in the vertical, while demonstrating a self-similarity in their time scales by being related through a power-law distribution. The inclination angle is inferred from the vertical shifts in the peak positions of the cross-correlation coefficients. However, in the second regime, the vertical inclination disappears for the temperature structures with hardly any change observed for the moisture. Moreover, the power-law exponents of the turbulent temperature time scales remain sensitive to the regimes, although no such effect is visible in the power-law character of the moisture time scales. Additionally, the dissimilarity in the heat and moisture transport is investigated through a novel polar-quadrant based approach that separates phases and amplitudes of the flux-transporting motions.