The topic of polymers with dynamic bonds (stickers) appears as an exciting and promising area of materials science, thanks to their attractive self-healable, recyclable, extremely tough, and super extensible properties. Polymers with phase separated dynamic bonds revealed several unique properties, but mechanisms controlling their viscoelastic properties remain poorly understood. In this work, we present a dynamic analysis of a model polymer system with phase separated hydrogen bonding functionalities. The results confirm that terminal relaxation in these systems is independent of polymer segmental dynamics and is instead controlled by structural relaxations in clusters of stickers. Detailed analysis revealed a surprising result: terminal relaxation time of these systems has weaker temperature dependence than that of structural relaxation in clusters, although the former is slower than the latter. Borrowing ideas from the field of block copolymers, we ascribed this unusual result to an LCST-like behavior for the miscibility of the stickers in the polymer matrix. The presented results and ideas deepen the understanding of the viscoelasticity for polymers with dynamic bonds, enabling intelligent design of functional materials with desired macroscopic properties.