We consider quark-hadron duality relations and QCD sum rules for correlators involving exotic tetraquark currents, here specializing to the case of quark-exchange processes. We point out the differences they exhibit with respect to the cases involving ordinary bilinear quark currents. Based on the observation that only diagrams possessing at least four-quark singularities can contribute to the formation of tetraquark states, we show that the quark-hadron duality relations and the corresponding sum rules split into two nonoverlapping relations. The ultimate tetraquark-adequate QCD sum rule is concerned only with one of these relations, in which the operator product expansion starts with diagrams of order $O\left({\alpha }_s^2\right)$.