Quantum time crystals are systems characterized by spontaneously emerging periodic order in the time domain1. While originally a phase of broken time translation symmetry was a mere speculation2, a wide range of time crystals has been reported3,4,5. However, the dynamics and interactions between such systems have not been investigated experimentally. Here we study two adjacent quantum time crystals realized by two magnon condensates in superfluid 3He-B. We observe an exchange of magnons between the time crystals leading to opposite-phase oscillations in their populations—a signature of the AC Josephson effect6—while the defining periodic motion remains phase coherent throughout the experiment. Our results demonstrate that time crystals obey the general dynamics of quantum mechanics and offer a basis to further investigate the fundamental properties of these phases, opening pathways for possible applications in developing fields, such as quantum information processing.