In astronomical surveys, such as the Zwicky Transient Facility (ZTF), supernovae (SNe) are relatively uncommon objects compared to other classes of variable events. Along with this scarcity, the processing of multi-band light-curves is a challenging task due to the highly irregular cadence, long time gaps, missing-values, low number of observations, etc. These issues are particularly detrimental for the analysis of transient events with SN-like light-curves. In this work, we offer three main contributions. First, based on temporal modulation and attention mechanisms, we propose a Deep Attention model called TimeModAttn to classify multi-band light-curves of different SN types, avoiding photometric or hand-crafted feature computations, missing-values assumptions, and explicit imputation and interpolation methods. Second, we propose a model for the synthetic generation of SN multi-band light-curves based on the Supernova Parametric Model (SPM). This allows us to increase the number of samples and the diversity of the cadence. The TimeModAttn model is first pre-trained using synthetic light-curves in a semi-supervised learning scheme. Then, a fine-tuning process is performed for domain adaptation. The proposed TimeModAttn model outperformed a Random Forest classifier, increasing the balanced-F 1 score from ≈ .525 to ≈ .596. The TimeModAttn model also outperformed other Deep Learning models, based on Recurrent Neural Networks (RNNs), in two scenarios: late-classification and early-classification. Finally, we conduct interpretability experiments. High attention scores are obtained for observations earlier than and close to the SN brightness peaks, which are supported by an early and highly expressive learned temporal modulation.