  Binary discrete nonlinear Schr\"odinger equation is used to describe dynamics
of two-species Bose-Einstein condensate loaded into an optical lattice. Linear
inter-species coupling leads to Rabi transitions between the species. In the
regime of strong nonlinearity, a wavepacket corresponding to condensate
separates into localized and ballistic fractions. Localized fraction is
predominantly formed by immiscible solitons consisted of only one species.
Initial states without spatial separation of occupied sites expose formation of
immiscible solitons after a strongly chaotic transient. We calculate the
finite-time Lyapunov exponent as a rate of wavepacket divergence in the Hilbert
space. Using the Lyapunov analysis supplemented by Monte-Carlo sampling, it is
shown that appearance of immiscible solitons after the chaotic transient
corresponds to self-stabilization of the wavepacket. It is found that onset of
chaos is accompanied by fast variations of kinetic and interaction energies.
Crossover to self-stabilization is accompanied by reduction of condensate
density due to emittance of ballistically propagating waves. It turns out that
spatial separation of species should be a necessary condition for wavepacket
stability in the presence of linear inter-species coupling.
