We have performed ab initio molecular dynamics (MD) simulations to study the alkali-metal dynamics in the Al-doped (KAl0.33W1.67O6 and RbAl0.33W1.67O6) and undoped (KW2O6 and RbW2O6) defect pyrochlore tungstates. The K atoms exhibit novel rattling dynamics in both the doped and undoped tungstates while the Rb atoms do not. The KAl0.33W1.67O6 experimental thermal conductivity curve shows an unusual depression between ~ 50 K and ~ 250 K, coinciding with two crossovers in the K dynamics: the first at ~ 50 K, from oscillatory to diffusive, and the second at ~ 250 K, from diffusive back to oscillatory. We found that the low-temperature crossover is a result of the system transitioning below the activation energy of the diffusive dynamics whereas the high-temperature crossover is driven by a complex reconstruction of the local potential around the K atoms due to the cage dynamics.This leads to a hardening of the K potential with increasing temperature. This unusual reconstruction of the potential may have important implications for the interpretation of finite-temperature dynamics based on zero-temperature potentials in similar materials. The key result is that the novel K rattling, involving local diffusion, leads to a significant reduction in the thermal conductivity. We suggest that this may open a new route in the phonon engineering of cage compounds for thermoelectric materials where the rattlers are specifically selected to reduce the lattice thermal conductivity by the mechanism of local diffusion. a)