In this work we present a comprehensive study of the spin dynamics and fluctuations in the ordered magnetic phases of the prototype multiferroic material TbMnO₃. From the temperature dependence of the dynamical and static components of the time-dependent asymmetry, we demonstrate the existence of strong local magnetic-field disorder arising from the modulated Mn³⁺ spin arrangement and the effect of the Tb³⁺ ordering at low temperatures. We provide evidence for an unusual magnetostructural coupling in the paramagnetic phase of TbMnO₃ by means of muon spin spectroscopy. No short-range magnetic ordering definitively occurs in the paramagnetic phase and the unusual properties found in the temperature dependence of the magnetic susceptibility are due to a magnetostructural coupling, likely involving oxygen displacements.