A time crystal is a macroscopic quantum system in periodic motion in its ground state, stable only if isolated from energy exchange with the environment. For this reason, coupling separate time crystals is challenging, and time crystals in a dynamic environment have yet not been studied. In our experiments, two coupled time crystals made of spin-wave quasiparticles (magnons) form a macroscopic two-level system. The two levels evolve in time as determined intrinsically by a nonlinear feedback. Magnons move from the ground level to the excited level driven by the Landau-Zener effect, combined with Rabi population oscillations. We thus demonstrate how to arrange spontaneous dynamics between interacting time crystals. Our experiments allow access to every aspect and detail of the interaction in a single run of the experiment, inviting technological exploitation-- potentially even at room temperature.