Recently, research on biomaterials has been focused on the development of platforms able to mimic the three-dimensional microenvironment of cells with bioactive signals to support cellular processes such as cell adhesion, proliferation and differentiation. In this regard, there is an increased interest in the use of hydrogels—particularly with the confinement of bioactive cues at the microscale—to mimic the cell niche through accurate control of cell-to-cell and cell–material interactions. In this work, we propose the design and fabrication of bioactive microgels containing sodium alginate loaded with calcium phosphate particles with micro- or sub-micrometric sizes via electrohydrodynamic atomization (EHDA) for use as in vitro models of hard tissue regeneration. Different processing strategies, from physical entrapment to in situ precipitation, were optimized. Morphological analyses (optical, SEM, TEM, and MicroCT) showed a narrow distribution of perfectly rounded particles with different spatial distributions of calcium phosphates and average diameters ranging from 223 ± 18 µm to 850 ± 64 µm as a function of mineral phase content and EHDA process conditions. Chemical/physical analyses (FTIR, TGA, and EDS) confirmed the presence of calcium phosphates in terms of chemical composition (i.e., Ca/P ratio) and relative volume fraction. In vitro studies were carried out to thoroughly investigate the response of dental pulp mesenchymal stem cells (DP-MSCs). Results demonstrated that the presence of calcium phosphates with different chemical compositions and/or particle sizes play an active role in the mechanisms of cells in terms of increased proliferation for up to 14 days and mineralization, as shown by alkaline phosphatase activity, thus contributing to mimicking the cell microenvironment. These results are promising for the development of in vitro models for the study of cellular behavior and for use as bioactive scaffolds for the regeneration of hard tissues, such as bone or dental-pulp complexes.