We present and analyze ALMA submillimeter observations from a multi-wavelength campaign of Sgr A* during 18 July 2019. In addition to the submillimeter, we utilize concurrent mid-IR (Spitzer) and X-ray (Chandra) observations. The submillimeter emission lags $delta t=21.48^{+3.44}_{-3.57}$ minutes behind the mid-IR data. The entire submillimeter flare was not observed, raising the possibility that the time delay is a consequence of incomplete sampling of the light curve. The decay of the submillimeter emission is not consistent with synchrotron cooling. Therefore, we analyze these data adopting an adiabatically expanding synchrotron source that is initially optically thick or thin in the submillimeter, yielding time-delayed or synchronous flaring with the IR, respectively. The time-delayed model is consistent with a plasma blob of radius $0.8~R_{text{S}}$ (Schwarzschild radius), electron power-law index $p=3.5$ ($N(E)propto E^{-p}$), equipartition magnetic field of $B_{text{eq}}approx90$ Gauss, and expansion velocity $v_{text{exp}}approx0.004c$. The simultaneous emission is fit by a plasma blob of radius $2~R_{text{S}}$, $p=2.5$, $B_{text{eq}}approx27$ Gauss, and $v_{text{exp}}approx0.014c$. Since the submillimeter time delay is not completely unambiguous, we cannot definitely conclude which model better represents the data. This observation presents the best evidence for a unified flaring mechanism between submillimeter and X-ray wavelengths and places significant constraints on the source size and magnetic field strength. We show that concurrent observations at lower frequencies would be able to determine if the flaring emission is initially optically thick or thin in the submillimeter.
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