We study numerically the evolution of the cavity electromagnetic field mode which is in resonance with an oscillating boundary (dynamical Casimir effect), taking into account the interaction between the field and a two-level atom, that may or not be continuously monitored by a coupled atomic excitation detector. We analyze the behavior of the field statistics and the quadrature squeezing properties in different regimes, demonstrating that at the expense of decreasing the number of produced photons and the degree of squeezing, one can create qualitatively new types of cavity field states. ► We study the statistics of photons created in a cavity via dynamical Casimir effect. ► We take into account the interaction with a two-level atom placed inside the cavity. ► The field–atom dynamics is calculated numerically for the Rabi coupling. ► The interaction with a detector can totally change the statistics of created photons. ► The statistics can vary from weakly super-Poissonian to strong “hyper-Poissonian”.