The recent progress in deep learning also makes one reconsider the reality that architecturally more complicated models tend to perform better at hydrological forecasting. Despite the common belief that Long Short-Term Memory (LSTM) models are useful in rainfall-runoff models, the transferability to the reservoirs that are managed by deterministic operation rules is understudied. In this article, we do a comparative study of Physics-Informed Bi-Directional LSTM with Temporal Attention and a Random Forest (RF) algorithm to daily predict a reservoir outflow in Shasta Dam and Oroville Dam located in California. To reduce the difficulty associated with low density measurements, we combine NASA POWER satellite data with ground-based measurements and thus they enhance the dataset. The physics-informed properties, one of which is the mass-balance proxies and another one is seasonal encodings, are used to secure the models into a system of physical consistency. Empirical findings also show that the Random Forest model performs better in terms of Nash-Sutcliffe Efficiency scores of 0.909 in Shasta Dam and 0.683 in Oroville Dam compared to the Bi-LSTM scores of 0.827 and 0.681, respectively. Ensemble approaches, including the Random Forest, seem to be more accurate in modelling the rule-of-thumb operational regimes of the reservoirs, but the deep-learning approach tends to regulate the changes dynamics of transition issues related to outflow releases. The totality of these results implies that in the case of rule-dominated reservoir systems, the simpler ensemble learning approaches may even perform better than the sophisticated deep-learning systems. In this regard, the selection of the model must be driven by the correspondence with the characteristics of the system, but not the bias with the architectural elaboration.