The study of superconducting materials that also possess nontrivial correlations or interactions remains an active frontier of condensed matter physics. NbSe$_2$ belongs to this class of superconductors and recent research has focused on the two-dimensional properties of this layered material. Here an investigation of the superconducting-to-normal-state transition in NbSe$_2$ is detailed, and found to be driven by dynamically-created vortices. Under the application of RF radiation, these vortices allow for two novel Josephson effects to be observed. The first is a coupling between Josephson currents and charge density waves in phase-slip junctions. The second is the Josephson detection of multi-band superconductivity, which is revealed in an anomalous magnetic field and RF frequency response of the AC Josephson effect. Our results shed light on the nature of superconductivity in this material, unearthing exotic phenomena by exploiting nonequilibrium superconducting effects in atomically-thin materials.