Using the time-dependent density functional theory at the X3LYP/6-31++G(d,p)/SMD level, the vibronic absorption spectrum of the thiazine dye Azure A (AA) in an aqueous solution was calculated. This study is a logical continuation of the previously published work [L.O. Kostjukova et al. Int. J. Quantum Chem. (2021) e26662], in which the water environment of AA was set implicitly in the continuum approximation using the SMD model. In the present work, we used a combined setting of the aqueous environment: three water molecules were explicitly described, forming strong hydrogen bonds with a dye molecule; the rest of the aqueous medium was set implicitly, also by the SMD method. This approach was used to elucidate the effect of site-specific interactions with a solvent on both the ground and excited states of the dye molecule and on the transition between them (solvatochromism). The reverse effect of excitation of the AA molecule on its nearest hydration shell was also of interest. Calculations have shown that there is an increase in these H-bonds upon photoexcitation of the dye. In this case, the maximum of the vibronic absorption spectrum AA undergoes a bathochromic shift by 15 nm. These results were analyzed from the point of view of the solvatochromic theory. Frontier molecular orbitals, between which an electronic transition occurs, and maps of the distribution of electron density and electrostatic potential of the ground and excited states of the "AA+3H2O" system have been built. The photoinduced polarization of the dye molecule was analyzed.