  We analyze the spin dynamics of an out-of-equilibrium large spin dipolar
atomic Bose gas in an optical lattice. We observe a smooth crossover from a
complex oscillatory behavior to an exponential behavior throughout the Mott to
superfluid transition. While both of these regimes are well described by our
theoretical models, we provide data in the intermediate regime where dipolar
interactions, contact interactions, and super-exchange mechanisms compete. In
this strongly correlated regime, spin dynamics and transport are coupled, which
challenges theoretical models for quantum magnetism.
