New fluorescent dyes containing an assembled 1,4-dihydroazolo[5,1-c][1,2,4]triazine (DAT) core and an isoxazole ring were synthesized through a reaction between diazopyrazole or diazoimidazoles and isoxazolyl-derived enamines in mild conditions. The photophysical characteristics (maxima absorption and emission, Stokes shifts, fluorescent quantum yields, and fluorescence lifetimes) of the new fluorophores were obtained. The prepared DATs demonstrated emission maxima ranging within 433–487 nm, quantum yields within 6.1–33.3%, and a large Stokes shift. The photophysical characteristics of representative DAT examples were studied in ten different solvents. Specific (hydrogen bonds) and non-specific (dipole–dipole) intermolecular and intramolecular interactions were analyzed using XRD data and spectral experiments. Solvatochromism was analyzed using Lippert–Mataga and Dimroth–Reichardt plots, revealing the relationship between the DAT structure and the nature of solute–solvent interactions. The significant advantages of DATs are the fluorescence of their powders (QY up to 98.7%). DAT-NMe2 10 expressed bright aggregation-induced emission (AIE) behavior in DMSO and THF as the water content increased. The numerous possible variations of the structures of the heterocycles included in the DATs, as well as substituents, create excellent prospects for adjusting their photophysical and physicochemical properties.