The first extended series of observations of Saturn's auroral emissions, undertaken by the Hubble Space Telescope in January 2004 in conjunction with measurements of the upstream solar wind and interplanetary magnetic field (IMF) by the Cassini spacecraft, have revealed a strong auroral response to the interplanetary medium. Following the arrival of the forward shock of a corotating interaction region compression, bright auroras were first observed to expand significantly poleward in the dawn sector such that the area of the polar cap was much reduced, following which the auroral morphology evolved into a spiral structure around the pole. We propose that these auroral effects are produced by compression-induced reconnection of a significant fraction of the open flux present in Saturn's open tail lobes, as has also been observed to occur at Earth, followed by subcorotation of the newly closed flux tubes in the outer magnetosphere region due to the action of the ionospheric torque. We show that the combined action of reconnection and rotation naturally gives rise to spiral structures on newly opened and newly closed field lines, the latter being in the same sense as observed in the auroral images. The magnetospheric corollary of the dynamic scenario outlined here is that corotating interaction region-induced magnetospheric compressions and tail collapses should be accompanied by hot plasma injection into the outer magnetosphere, first in the midnight and dawn sector, and second at increasing local times via noon and dusk. We discuss how this scenario leads to a strong correlation of auroral and related disturbances at Saturn with the dynamic pressure of the solar wind, rather than to a correlation with the north-south component of the IMF as observed at Earth, even though the underlying physics is similar, related to the transport of magnetic flux to and from the tail in the Dungey cycle.