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Résumé : Breakthrough curves (BTCs) record arrival times, but anomalous transport models are often fitted with time-normalized spatial concentration profiles. Here, the effect of this mismatch on groundwater-transport upscaling is tested. Analytical limits and high-$q$ scaling were verified first. Six first-passage models were then fitted to particle arrivals from 36 two-dimensional digital aquifer runs. The set included exact ADE, $q$ and time-memory extensions, a joint memory-$q$ model, Gamma-CTRW, and a two-path inverse-Gaussian mixture. After the operator was corrected, memory-qFPT was not selected in any run. AICc selected the two-path model in 20 runs, Gamma-CTRW in 15, and q-FPT in one. Median downstream holdout log-RMSE was 0.904, 0.914, and 0.959 for the two-path, Gamma-CTRW, and memory-qFPT models, respectively. The memory-$q$ parameters also failed an independent plume-scaling test ($R^2=0.189$; slope $=-0.332$). Meanwhile, multimodal downstream BTCs increased from 0\% in homogeneous media to 100\% in the strongest heterogeneity class. Gamma-CTRW was also favored in an independent synthetic field. Observation consistency is therefore necessary but not sufficient for physical validation. In these simulations, pathway and waiting-time structure was supported more strongly than a unique memory-$q$ law.