The nontrivial properties of interband spin fluctuations are studied by the random phase approximation in a Hubbard model describing the molecular conductor α-(BEDT-TTF)₂I₃, where wave functions are based on the four sublattices named A, A′, B, and C in a two-dimensional BEDT-TTF molecular plane. It is found that the ferrimagnetic polarization observed by a recent NMR measurement emerges only if there exist cross terms among intra- and inter-band irreducible susceptibility matrix elements in the presence of the on-site Coulomb interaction U. It is also found that the nontrivial sign of the interband components of the spin susceptibility, being negative only for the B sublattice, is closely related to the characteristic phase structure of wave functions in the Dirac fermion system with multisublattices. The negative value of the spin susceptibility on the B sublattice observed in the experiment is associated with this negative interband susceptibility, which comes from the excitations in the gentle-slope region of the energy dispersion connecting the Dirac points with saddle points in the first Brillouin zone.

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