In phases III and IV of Cs3H(SeO4)2, the vibrational state and intrabond transfer of the proton in the dimeric selenates are systematically studied with a wide range of absorbance spectra, a spin-lattice relaxation rate of 1H-NMR (T1 -1), and DFT calculations. The OH stretching vibrations have extremely broad absorption at around 2350 (B band) and 3050 cm-1 (A band), which originate from the 0-1 and 0-2 transitions in the asymmetric double minimum potential, respectively. The anharmonic-coupling calculation makes clear that the A band couples not only to the libration but also to the OH bending band. The vibrational state (nano-second order) is observed as the response of the proton basically localized in either of the two equivalent sites. The intrabond transfer between those sites (pico-second order) yields the protonic fluctuation reflected in T1 -1. Together with the anomalous absorption [νp2 phonon, libration, tetrahedral deformation (δ440), and 610-cm-1 band], we have demonstrated that the intrabond transfer above 70 K is dominated by the thermal hopping that is collectively excited at 610 cm-1 and the phonon-assisted proton tunneling (PAPT) relevant to the tetrahedral deformation [PAPT(def)]. Below 70 K, T1 -1 is largely enhanced toward the antiferroelectric ordering and the distinct splitting emerges in the libration, which dynamically modulates the O(2)-O'(2) distance of the dimer. The PAPT(lib) associated with the libration is confirmed to be a driving force of the AF ordering.