We previously reported that two analogues of the Photoactive Yellow Protein chromophore, trans-phydroxycirmarnic acid (pCA(2-)) and its amide derivative (pCM(-)) in their deprotonated forms, undergo a trans-cis photoisomerization whereas the thioester derivative, trans-p-hydroxythiophenyl cinnamate (pCT(-)), does not. pCT- is also the only one to exhibit a short-lived intermediate on its excited-state deactivation pathway. We here further stress the existence of two different relaxation mechanisms for these molecules and examine the reaction coordinates involved. We looked at the effect of the solvent properties (viscosity, polarity, solvation dynamics) on their excited-state relaxation dynamics, probed by ultrafast transient absorption spectroscopy. Sensitivity to the solvent properties is found to be larger for pCT- than for pCA2- and pCM-. This difference is considered to reveal that either the relaxation pathway or the reaction coordinate is different for these two classes of analogues. It is also found to be correlated to the electron donor-acceptor character of the molecule. We attribute the excited-state deactivation of analogues bearing a weaker acceptor group, pCA(2-) and pCM(-), to a stilbene-like photoisomerization mechanism with the concerted rotation of the ethylenic bond and one adjacent single bond. For pCT-, which contains a stronger acceptor group, we consider a photoisomerization mechanism mainly involving the single torsion of the ethylenic bond. The excited-state deactivation of pCT(-) would lead to the formation of a ground-state intermediate at the "perp" geometry, which would return to the initial trans conformation without net isomerization.