  We study the dynamics of binary Bose-Einstein condensates made of ultracold
and dilute alkali-metal atoms in a quasi-one-dimensional setting. Numerically
solving the two coupled Gross-Pitaevskii equations which accurately describe
the system dynamics, we demonstrate that the spin transport can be controlled
by suitably quenching spin-orbit (SO) and Rabi coupling strengths. Moreover, we
predict a variety of dynamical features induced by quenching: broken
oscillations, breathers-like oscillating patterns, spin-mixing-demixing,
miscible-immiscible transition, emerging dark-bright states, dark solitons, and
spin-trapping dynamics. We also outline the experimental relevance of the
present study in manipulating the spin states in $^{39}$K condensates.
