We study the dynamics of macroscopically coherent matter waves of an ultracold atomic spin-1 or spinor condensate on a ring lattice of six sites and demonstrate the spatiotemporal internal Josephson effect. Using a discrete solitary mode of uncoupled spin components as an initial condition, the time evolution of this many-body system is found to be characterized by two dominant frequencies leading to quasiperiodic dynamics at various sites. The dynamics of spatially averaged and spin-averaged degrees of freedom, however, is periodic enabling a unique identification of the two frequencies. By increasing the spin-dependent atom-atom interaction strength we observe a resonance state, where the ratio of the two frequencies is a characteristic integer multiple and the spin-and-spatial degrees of freedom oscillate in "unison". Crucially, this resonant state is found to signal the onset of chaotic dynamics characterized by a broadband spectrum. In a ferromagnetic spinor condensate with attractive spin-dependent interactions, the resonance is accompanied by a transition from oscillatory-to rotational-type dynamics as the time evolution of the relative phase of the matter wave of the individual spin projections changes from bounded to unbounded. DOI: 10.1103/PhysRevA.87.033608