Behavior Model Inference techniques aim at mining behavior models from execution traces. While most of approaches usually ground on local similarities in traces, recent work, referred to as behavior mining with temporal steering, propose to include long term dependencies in the mining process. Such dependencies correspond to temporal implications between events in execution traces, whose consideration allows to ensure a better consistency of the extracted model. Nevertheless, the existing approaches are usually limited by their high computational complexity and the approximations to reduce the cost of temporal rules checking. This paper revisits behavior mining with temporal steering by defining an efficient algorithm that performs an exact consideration of the observed dependencies: in our experiments, greatly reduced processing times (from exponential to quasi-linear) for exact mining with temporal steering have been observed. Furthermore, beyond highlighting the great benefits of considering temporal dependencies, this paper also proposes new key extensions to the existing work that allow to include more complex dependencies in the mining process. Intensive evaluation finally demonstrates the great performances of the proposed approach.