In this paper, we present a comprehensive study of magnetic dynamics in the rare-earth orthoferrite YbFeO₃ at temperatures below and above the spin-reorientation (SR) transition T_SR=7.6 K, in magnetic fields applied along the a, b, and c axes. Using single-crystal inelastic neutron scattering, we observed that the spectrum of magnetic excitations consists of two collective modes well separated in energy: 3D gapped magnons with a bandwidth of ∼60meV, associated with the antiferromagnetically (AFM) ordered Fe subsystem, and quasi-1D AFM fluctuations of ∼1meV within the Yb subsystem, with no hybridization of those modes. The spin dynamics of the Fe subsystem changes very little through the SR transition and could be well described in the frame of semiclassical linear spin-wave theory. On the other hand, the rotation of the net moment of the Fe subsystem at T_SR drastically changes the excitation spectrum of the Yb subsystem, inducing the transition between two regimes with magnon and spinonlike fluctuations. At T < T_SR only a gapped broad spinonlike continuum dominates the spectrum. In this work we show that a weak quasi-1D coupling within the Yb subsystem J_Yb-Yb, mainly neglected in previous studies, creates unusual quantum spin dynamics on the low-energy scales. The results of our work may stimulate further experimental search for similar compounds with several magnetic subsystems and energy scales, where low-energy fluctuations and underlying physics could be "hidden" by a dominating interaction.