We study fluctuations of the sigma field and the net-baryon number on the crossover side of the critical point within the model of nonequilibrium chiral fluid dynamics (N χ FD). Herein, the sigma field as the chiral order parameter is propagated explicitly and coupled to a fluid of quarks. Before investigating these fluctuations in an expanding nonequilibrium medium, we scrutinize the N χ FD model by comparing cumulants of the sigma fluctuations in a thermalized box to (ratios of) susceptibilities as they are obtained from derivatives of the grand canonical potential. The dynamically determined cumulants follow the trend of the thermodynamic susceptibilities. In an expanding inhomogeneous medium, however, the behavior of the fluctuations is shown to be different as a result of memory effects.