We discuss the question whether inner core (IC) differential rotation or temporal change of the IC surface provides a consistent interpretation for temporal changes of the IC‐related phases and their coda. While temporal change of the IC surface is required and provides a consistent explanation to all the seismic observations, we present three lines of seismic evidence showing that IC differential rotation cannot provide a consistent or reasonable interpretation for the observed temporal change of seismic waves from repeating earthquakes in the South Sandwich Islands (SSI) and the Middle America subduction zone. (1) Changed PKIKP/PKiKP coda between events in a doublet in SSI indicates an IC surface scatterer that simply disappeared, with no associated energy in the later event for any assumed IC differential rotation. (2) Within a cluster in SSI, comparisons between temporal changes of PKIKP wave and its coda of the earlier and later event pairs yield contradictory estimates of differential rotation rate change by a factor of at least 27, using different portions of seismic data. (3) The seismic data from repeating earthquakes in Middle America indicate a PKiKP temporal change of 0.017–0.04 s on a timescale of 8–85 days, requiring an unreasonable rotation rate of at least 8.6°/year. We conclude that the observed temporal changes of IC phases are caused by temporal changes of the IC surface, which occur in some localized regions within a timescale of days or months, a phenomenon that should provide important clues to our understanding of core dynamics.