Turbulent plasmas notably self-organize to higher energy states upon application of additional free energy sources or modification of edge operating conditions. Mechanisms whereby such bifurcations occur have been actively debated for decades, mostly on the basis of reduced models. Here we unravel a surprising causal chain of events in the onset of an improved confinement state, by applying generic entropy-based and information theoretic measures to the primitive kinetic equations. Interfacial contamination of a large, stable region (the ‘dog’) by locally-borne peripheral turbulent fluctuations (the ‘tail’) is found to be central to explaining transport properties, globally. These results, highly relevant to the quest for magnetic fusion advocate the use of such data-driven methods to many problems in fluids and plasmas where interfacial turbulent contamination is active.