  Sagittarius A$^\ast$ is a compact radio source at the center of the Milky Way
that has not conclusively shown evidence for the presence of a relativistic
jet. Nevertheless, indirect methods at radio frequencies do indicate consistent
outflow signatures. Temporal shifts between features in frequency bands are
known as time lags, associated with flares or outflows of the accretion system.
It is possible to gain information on the emission and outflow mechanics by
interpreting these time lags. By means of a combined general-relativistic
magnetrohydrodynamical and radiative transfer modeling, we study the origin of
the time-lags for magnetically arrested disc models at three black hole spins
($a_\ast \in \{ -0.9375, 0, 0.9375 \}$). We exclusively modeled the emission
from the source across a frequency range of $\nu$ = 19-47 GHz. Our study also
includes a targeted `slow light' study for one of the best-fitting `fast light'
windows. We recovered the observational time-lag relations in various windows
of our simulated light curves. The theoretical interpretation of these most
promising time-lag windows is threefold; i) a magnetic flux eruption perturbs
the jet-disc boundary and creates a flux tube, ii) the flux tube orbits and
creates a clear emission feature, and iii) the flux tube interacts with the
jet-disc boundary. The best-fitting windows have an intermediate
(i=30$^\circ$/50$^\circ$) inclination and zero-BH-spin. The targeted `slow
light' study did not yield better-fitting time-lag results, which indicates
that the fast vs. slow light paradigm is often not intuitively understood and
is likely influential in timing-sensitive studies. Sophisticated
general-relativistic magnetrohydrodynamical models consistently capture the
observational time-lag behavior, which is rooted in the complex dynamic
interplay between the flux tube and coupled disk-jet system.
