  The Transiting Exoplanet Survey Satellite (TESS) is NASA's latest space
telescope dedicated to the discovery of transiting exoplanets around nearby
stars. Besides the main goal of the mission, asteroseismology is an important
secondary goal and very relevant for the high-quality time series that TESS
will make during its two year all-sky survey. Using TESS for asteroseismology
introduces strong timing requirements, especially for coherent oscillators.
Although the internal clock on board TESS is precise in its own time, it might
have a constant drift and will thus need calibration, or offsets might
inadvertently be introduced. Here we present simultaneously ground- and
space-based observations of primary eclipses of several binary systems in the
Southern ecliptic hemisphere, used to verify the reliability of the TESS
timestamps. From twelve contemporaneous TESS/ground observations we determined
a time offset equal to 5.8 +/- 2.5 sec, in the sense that the Barycentric time
measured by TESS is ahead of real time. The offset is consistent with zero at
2.3-sigma level. In addition, we used 405 individually measured mid-eclipse
times of 26 eclipsing binary stars observed solely by TESS to test the
existence of a potential drift with a monotonic growth (or decay) affecting the
observations of all stars. We find a drift corresponding to sigma_drift = 0.009
+/- 0.015 sec/day. We find that the measured offset is of a size that will not
become an issue for comparing ground-based and space data for coherent
oscillations for most of the targets observed with TESS.
