Minimizing the energy difference between the lowest singlet (S-1) and the lowest triplet states, Delta E-ST, is the main strategy to design thermally activated delayed fluorescence (TADF) molecules, and spatially separating the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is the general method in the design. However, such a separation also tends to reduce the oscillator strength of the S-1 state. In real systems, vibrations change the S-1 oscillator strength, and thus one needs to consider the vibronic coupling toward searching for TADF candidate molecules. Here, we evaluate the importance of vibronic coupling by including the first-order perturbative correction to the transition dipole moments of carbazolyl-phthalonitrile derivatives. Indeed, some molecules display large enhancements in their oscillator strengths, with their fluorescence lifetimes reduced by 2 orders of magnitude. The twisting mode between the carbazole groups and phthalonitrile is the most important mode in inducing the perturbations. Thus, performing the perturbative correction is crucial in attaining more reliable predictions on their fluorescence propensities. We also observe that some other molecules, whose zeroth-order predicted fluorescence rates are much slower than the actual experimental data, are affected little by the same first-order correction. For these molecules, we deduce that the geometry-dependent excited-state switching kicks in. Our results demonstrate the significance of vibronic coupling in TADF molecules and the importance of adopting correction schemes as the guidelines for screening of useful TADF molecules.