  We study the critical properties of net-baryon-number fluctuations at the
chiral restoration transition in a medium at finite temperature and net baryon
density. The chiral dynamics of quantum chromodynamics (QCD) is modeled by the
Polykov-loop extended Quark-Meson Lagrangian, that includes the coupling of
quarks to vector meson and temporal gauge fields. The Functional
Renormalization Group is employed to properly account for the $O(4)$
criticality at the phase boundary. We focus on the properties and systematics
of ratios of the net-baryon-number cumulants $\chi_B^n$, for ${1\leq n\leq 6}$,
near the phase boundary. The results are presented in the context of the recent
experimental data of the STAR Collaboration on fluctuations of the net proton
number in heavy ion collisions at RHIC. We show that the model results for the
energy dependence of the cumulant ratios are in good overall agreement with the
data, with one exception. At center-of-mass energies below
${19.6\;\mathrm{GeV}}$, we find that the measured fourth-order cumulant
deviates considerably from the model results, which incorporate the expected
$O(4)$ and $Z(2)$ criticality. We assess the influence of model assumptions and
in particular of repulsive vector-interactions, which are used to modify the
location of the critical endpoint in the model, on the cumulants ratios.
Finally, we discuss a possibility to test to what extent the fluctuations are
affected by nonequilibrium dynamics by comparing certain ratios of cumulants.
