Recently, branching and click chemistry strategies have been combined to design a series of optically active chromophores built from triazole moieties. These triazole based multipolar chromophores have shown to be promising candidates for two-photon absorption (TPA) transparency optimization in perspective of optical limiting in the visible region. In this work, the nature of one- and two-photon absorption properties in a family of triazole based chromophores has been investigated using hybrid time dependent density functional theory (TD-DFT). We use recent extensions of TD-DFT to determine nonlinear optical responses, and Natural Transition Orbitals to analyze the underlying electronic processes. Our results are also interpreted in the framework of the Frenkel exciton model. In agreement with experimental data, we found that introducing triazole moiety into multibranched chromophores substantially modifies their optical behavior due to changes in electronic delocalization and charge-transfer properties between donating end-groups and branching center that can be controlled by the triazole ring. Structural conformations via modulation of the torsion between phenyl and triazole rings significantly alter excited state electronic structure. Moreover, isomer positioning also greatly influences both linear and nonlinear optical responses such as TPA. Our theoretical findings allow elucidating these differences and contribute to the general understanding of structure-property relations. Consequently, interplay of donor/acceptor strength, triazole regioisomerism, and branching are shown to provide flexible means allowing for precise tuning of both linear and nonlinear optical responses, thus opening new perspectives towards synergic TPA architectures.