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Context.Sagittarius A* (Sgr A^*), the supermassive black hole at the center of the Milky Way, provides a unique laboratory to study accretion dynamics and plasma processes near the event horizon. Aims.We investigated the variability and polarization properties of Sgr A^*using ALMA observations during the 2018 Event Horizon Telescope campaign. Methods.We analyzed high-cadence full-polarization light curves from ALMA at millimeter wavelengths, performed time-series analysis, and investigated the temporal behavior during an X-ray flare observed byChandraon 2018 April 24. The variability characteristics are compared with expectations from standard accretion flow models. Results.We find low variability in total intensity (σ/μ < 10%), but significantly higher variability in linear and circular polarization (∼30% and ∼50%, respectively). A time-series analysis reveals red-noise variability, with power spectral densities between −2 and −3 across all Stokes parameters. Polarized intensity shows stable intra-day timescales, while total intensity exhibits more variable timescales, suggesting distinct emission regions, with polarization likely arising from a coherent structure. On April 24, a statistically significant inter-band delay in polarized intensity coincides with a near-simultaneous X-ray and millimeter peak that deviates from the typical delayed flare scenario. This event also features enhanced millimeter variability and coherent polarization loop evolution. The observed simultaneity challenges standard models of transient synchrotron emission with cooling delays, favoring instead a scenario of continuous energy injection in an optically thin region. Conclusions.Our results offer new constraints on the physical mechanisms driving variability in Sgr A^*, and provide key observational input for refining theoretical models of accretion and plasma behavior in the vicinity of supermassive black holes.