Solute transport in unsaturated porous media is of interest in many engineering and environmental applications. The interplay between small-scale, local forces and the porous microstructure exerts a strong control on the transport of fluids and solutes at the larger, macroscopic scales. Heterogeneity in pore geometry is intrinsic to natural material across a large range of scales. This multiscale nature, and the intricate links between two-phase flow and solute transport, remain far from well understood, by and large. Here, we use Direct Numerical Simulation (DNS) to quantify the effects of correlated heterogeneity on solute transport during drainage under an unfavorable viscosity ratio. We find that increasing spatial correlations in pore sizes increases the size of the required Representative Elementary Volume (REV). We also show that increasing the correlation length enhances solute dispersivity through its impact on the spatial distribution of low-velocity (diffusion-dominated) and high-velocity (advection-dominated) regions. Fluid saturation is shown to directly affect diffusive mass flux among high-and low-velocity zones. Another indirect effect of correlated heterogeneity on solute transport is through its control of the drainage patterns via rearrangements of mobile-immobile zones. Our findings improve quantitative understanding of solute mixing and dispersion in unsaturated conditions, highly relevant to some of our most urgent environmental problems.