A Raman spectroscopic study of the high-frequency optical phonons in single crystals of the multiferroic system RMn2O5 (R=Bi, Eu, Dy) was performed. All studied materials show anomalous phonon shifts, below a new characteristic temperature for these materials, T*∼60–65 K. The sign and magnitude of such shifts appear to be correlated with the ionic radius of R, envolving from softenings for R=Bi to hardenings for R=Dy and showing an intermediary behavior for R=Eu. Additional phonon anomalies were identified below ∼TN∼40–43 K, reflecting the onset of long-range ferroelectric and/or magnetic order of the Mn sublattice. Complementary dc-magnetic susceptibility [χ(T)] measurements for BiMn2O5 up to 800 K yield a Curie-Weiss temperature θCW=−253(3) K, revealing a fairly large frustration ratio (∣θCW∣∕TN=6.3). Deviations of χ(T) from a Curie-Weiss paramagnetic behavior due to magnetic correlations were observed below temperatures of the order of ∣θCW∣, with the inverse susceptibility showing inflection points at ∼160 K and ∼T*. Supported by χ(T) data, the anomalous Raman phonon shifts below T* are interpreted in terms of the spin-phonon coupling, in a scenario of strong magnetic correlations. Overall, these results support significant magnetic frustration, introduce a new characteristic temperature (T*), and suggest a surprisingly rich behavior for the magnetic correlations in the paramagnetic phase of this system.