We explore the time evolution of quasi-1D two component Bose-Einstein condensates (BECs) following a quench from one component BECs with a ${rm U}(1)$ order parameter into two component condensates with a ${rm U}(1)shorttimes{rm Z}_2$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifing any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin polarized domains, which are far from the systems ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is fully consistent with our stochastic-projected Gross-Pitaevskii calculation.
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