A wind nebula generating extended X-ray emission was recently detected surrounding Swift J1834.9-0846. This is the first magnetar for which such a wind nebula was found. Here, we investigate whether there is a plausible scenario where the pulsar wind nebula (PWN) can be sustained without the need of advocating for additional sources of energy other than rotational. We do this by using a detailed radiative and dynamical code that studies the evolution of the nebula and its particle population in time. We find that such a scenario indeed exists: Swift J1834.9-0846's nebula can be explained as being rotationally powered, as all other known PWNe are, if it is currently being compressed by the environment. The latter introduces several effects, the most important of which is the appearance of adiabatic heating, being increasingly dominant over the escape of particles as reverberation goes by. The need of reverberation naturally explains why this is the only magnetar nebula detected and provides estimates for Swift 1834.9-0846's age.