The Bray-Liebhafsky (BL) reaction is one of the simplest chemical oscillators consisting initially of only three components. Despite this, its mechanism is unknown for more than 100 years due to the absence of selective, sensitive, and fast experimental techniques for following all of the involved intermediates. The modeling of the BL mechanism assumes presumably mass action kinetics "adjustable" to oscillatory solutions by the application of mathematical stability analysis and treating the system as homogeneous. Such a basically mathematical approach need not suggest physically realistic kinetic parameters and is not unique since a number of models can be proposed. Based on recent experimental and computational results, a new model of the BL oscillatory reaction mechanism is constructed by including heterogeneous processes occurring in the system. The same set of equations is able to demonstrate not only the oscillatory evolution but also mixing effects on the oscillatory dynamics, and non-oscillatory stepwise-iodine oxidation and can rationalize other effects described in literature. Thus, the paradigm of treating the BL oscillatory system as a homogeneous one, described by formal kinetics only, is extended for a better understanding of the chemistry of this apparently simple system. The introduced ideas of energy redistribution may contribute to establishing an improved conceptual base for considering other complex oscillators in various fields of science.