Hydraulic turbines with high efficiency over a wide range of operating conditions offer a much sought-after flexibility to electricity producers. However, some low-head turbines exhibit sharp losses of efficiency close to their peak efficiency discharge that are linked to draft tube flow separations whose causes remain misunderstood. This paper presents the latest results obtained in the scope of the BulbT project that focused on the flow dynamics related to the efficiency drop. The main objectives are to document the transient characteristics of the flow in the hub-wake region and investigate interactions between the core flow and wall separations to identify potential mechanisms explaining the efficiency drop. Using proper orthogonal decompositions of synchronized time-resolved velocity and pressure measurements, highly energetic modes representing stochastic perturbations across BulbT's draft tube are identified. These perturbations occur only for the discharges affected by the efficiency drop, past the best efficiency point. Despite the absence of near-wall velocity measurements, the modal decompositions provide evidence that the onset of the efficiency drop is the result of two independent types of flow separation that occur on opposite sides of the draft tube. Upstream separations are found to happen simultaneously with an asymmetric acceleration of the flow in a region surrounding the turbine's axis and the tip of the runner hub and become the most important contributor to the efficiency drop at the highest measured flow rate. Furthermore, the likeliness of observing one kind of flow separation increases after it has already occurred, pointing to a strong history effect.