Covert communications provide a stronger privacy protection than cryptography and physical-layer security (PLS). However, previous works on covert communications have implicitly assumed the validity of channel reciprocity, i.e., wireless channels remain constant or approximately constant during their coherence time. In this work, we investigate covert communications in the presence of a disco RIS (DRIS) deployed by the warden Willie, where the DRIS with random and time-varying reflective coefficients acts as a "disco ball", introducing timevarying fully-passive jamming (FPJ). Consequently, the channel reciprocity assumption no longer holds. The DRIS not only jams the covert transmissions between Alice and Bob, but also decreases the error probabilities of Willie's detections, without either Bob's channel knowledge or additional jamming power. To quantify the impact of the DRIS on covert communications, we first design a detection rule for the warden Willie in the presence of time-varying FPJ introduced by the DRIS. Then, we define the detection error probabilities, i.e., the false alarm rate (FAR) and the missed detection rate (MDR), as the monitoring performance metrics for Willie's detections, and the signal-to-jamming-plusnoise ratio (SJNR) as a communication performance metric for the covert transmissions between Alice and Bob. Based on the detection rule, we derive the detection threshold for the warden Willie to detect whether communications between Alice and Bob is ongoing, considering the time-varying DRIS-based FPJ. Moreover, we conduct theoretical analyses of the FAR and the MDR at the warden Willie, as well as SJNR at Bob, and then present unique properties of the DRIS-based FPJ in covert communications. We present numerical results to validate the derived theoretical analyses and evaluate the impact of DRIS on covert communications.