The high-Tc superconductor DyBa24Cu34O7-x (SC) and its oxygen deficient tetragonal non-superconducting counterpart (NSC) have been studied by DC magnetization measurements down to 0.3 K and by 161 Moessbauer spectroscopy down to 0.05 K. The low-temperature Dy3+ paramagnetic fluctuation rates also show the influence of these correlations. Magnetic ordering occurs within the Dy sublattices near 1 K. The Dy3+ saturated magnetic moments show fairly large distributions around mean values of 7.0 (SC) and 7.3 μB (NSC). These distributions are attributed to crystal field inhomogeneities linked to the sample microstructure. In the SC we compare the average field penetration at the Dy sites with the percentage of the bulk Meissner effect. This suggests that the supercurrents are such that they preferentially shield the rare earth sites.