In the substituted Nd1−xTbxFe3(BO3 )4 (x = 0.1 and x = 0.2), possessing almost easy-axis magnetic structure at low temperatures, an unusual two-step transition in fields along the trigonal c axis was observed by magnetization and single-crystal neutron diffraction studies. At the first step, only part of the Tb Ising-type moments flip to the c axis, which is accompanied by a significant deviation of the antiferromagnetic Fe spins from the c axis. At the second step, the remaining Tb moments flip and the Fe moments flop into the basal plane. The observed evolution is qualitatively explained by a model assuming small deviations of Tb moments from the trigonal axis due to local environment distortions, which leads to nonequivalence of the Tb ions with respect to effective Tb-Fe exchange and external field. Thus, an intrinsic “hidden” instability of the magnetic system in the magnetic field occurs.