We report on diffraction measurements on multiferroic which demonstrate that the Tb- and Mn-magnetic orders are coupled below the ferroelectric transition . For the magnetic propagation vectors (τ) for Tb and Mn are locked so that τTb=τMn, while below we find that τTb and τMn lock-in to rational values of and , respectively, and obey the relation . We explain this novel matching of wave vectors within the frustrated anisotropic next-nearest-neighbor Ising model coupled to a periodic external field produced by the Mn-spin order. The τTb=τMn behavior is recovered when Tb magnetization is small, while the regime is stabilized at low temperatures by a peculiar arrangement of domain walls in the ordered state of Ising-like Tb spins.