Donor-acceptor Stenhouse adducts (DASAs) are a very recent class of organic photoswitches that combine excellent properties, such as color and polarity change, a large structural modification, and excellent fatigue resistance. Despite their potential applications in different fields, very few studies have focused on rationalizing their electronic structure properties. Here, by means of different state-of-the-art theoretical methods, including solvent and vibrational effects, we show that while time dependent-density functional theory (TD-DFT) can qualitatively describe DASAs' excited states, multiconfigurational quantum chemistry methods along with dynamic electron correlation (CASPT2, NEVPT2) are required for a quantitative agreement with the experiment. This finding is reasoned based on the different charge transfer characteristics observed. Moreover, the TD-DFT computed two-photon absorption properties are reported and suggested to red-shift the absorption band, as required for biological applications.