Digital health portals increasingly depend on highly “popular” physicians to anchor user traffic and drive revenue. Existing work, however, (i) conflates popularity with a single behavioural cue (consultation count) and (ii) relies on linear or shallow machine-learning models. We introduce PopNet, a hybrid TabTransformer + GRU that fuses demographic, behavioural, visual-cue and temporal-momentum signals to predict a composite Popularity Index (PopIdx) built from four pillars: demand, monetary appreciation, social proof and visibility. Across a five-fold group-wise cross-validation on 19 200 physician-quarter snapshots, PopNet attains MAE ≈ 0.091, beating ElasticNet by >40 %. Nevertheless, modern tree ensembles still edge it out (LightGBM MAE ≈ 0.046). Integrated-Gradient explanations and a feature-family ablation reveal platform visibility (inv_rank) as the single most important driver of popularity, followed by raw patient demand and monetary gifts. Fairness audits show a modest 0.006 PopIdx MAE gap between genders; a simple inverse-propensity re-weighting halves this gap with <0.002 performance loss. The study provides actionable levers for platform managers and a reusable, bias-audited modelling pipeline for future research.