The emergence of small-scale urban distributed solar generation (DSG) has urged the exploration of site-adaptive forecasting models designed to accurately predict future power outputs for unseen DSGs. In such scenarios, with numerous DSGs spread across utility-scale cities and a lack of historical data, it is not economically viable to use conventional approaches that develop individual models for each DSG. Therefore, this work aims to tackle this real-world challenge by adapting the state-of-the-art, attention-based temporal fusion transformer (TFT) model to 188 real-world operational DSG data, thereby validating the generalizability of self-attention mechanism for multi-step time series forecasting. When adapted to unseen DSGs without training data, the experiment results demonstrate that the proposed solar TFT (STFT) improves by 11.07%, 17.58%, and 22.76% over the persistence model at the 10-, 20-, and 30-minute forecasts, respectively. Even when compared to representative deep-learning models, such as a long short-term memory model specialized in time series forecasting, STFT has demonstrated improved forecast accuracy, achieving 3.34%, 4.18%, and 5.85% enhancements at the 10-, 20-, and 30-minute forecast horizons, respectively. However, the model architecture of STFT is more complex, and the computational cost associated with it is relatively higher compared to other deep learning models. This trade-off between accuracy and computational efficiency should be considered in practical applications. The forecast performance is analyzed in three typical weather conditions, namely, clear, partly cloudy, and overcast. STFT demonstrates advantages in high variability periods, especially during weather transition periods, where reference models experience lagged predictions yielding relatively large errors.