Solute transport through highly heterogeneous geologic environments with connected pathways through high-conductivity material and lenses of low permeability often is not described well by a macroscopic advection-dispersion equation. An upscaled advection-dispersion model with a uniform velocity and dispersion coefficient does not predict the significant plume asymmetry and extended tailing often observed over finite distances in such environments. We investigate the hydrogeologic conditions under which an upscaled model must incorporate another mechanism to describe the extended tailing arising from slow advection through and diffusion into and out of low-permeability inclusions. We use high-resolution simulations to determine ground truth transport results for 84 hydrogeologic scenarios comprising distinct low-permeability lenses set into an otherwise homogeneous background. We compare the ability of two one-dimensional, fitted, upscaled models to reproduce the arrival time curves from the fully resolved simulations. The first model uses a macrodispersion coefficient to describe the spreading due to the low-permeability inclusions. The second model accounts for the effect of the geologic heterogeneity with a nonequilibrium mass transfer component. When the equivalent conductivity of a domain is less than or equal to the geometric mean conductivity, a macroscopic advection-dispersion model matches the results well. When the equivalent conductivity is greater than the geometric mean, however, another model may be needed to describe the solute tailing.