Short-term forecasting of aggregated human mobility flows supports urban planning, intelligent transportation systems, and emergency response, yet existing models often require substantial mobility history and learn spatial structure implicitly through grids or graphs. Time series foundation models provide strong temporal priors but typically lack explicit geographic and social conditioning for origin-destination interactions. We introduce TS-Mob, a framework that conditions a fine-tuned time series foundation model (TimesFM) forecaster on a gravity-inspired destination-attractiveness index that encodes geographic and social signals computed from open data (living population, centroid distances, and Overture POI counts), together with weather covariates. Evaluated on commonly used benchmarks like Bike New York City, Taxi Beijing, and a nation-scale Spain origin-destination matrix estimated through mobile phone data, TS-Mob outperforms classical, deep spatio-temporal, and a set of foundation model-based baselines across RMSE, MAE, and CPC, with gains up to 78.71% lower MAE and 137.93% higher CPC over the best classical baseline, and up to about 4.27% lower RMSE over the strongest foundation baseline. Stratified analyses further show robustness across different temporal regimes, like weekdays/weekends.

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