Purpose: Surgery scene understanding with tool-tissue interaction recognition and automatic report generation can play an important role in intra-operative guidance, decision-making and postoperative analysis in robotic surgery. However, domain shifts between different surgeries with inter and intra-patient variation and novel instruments' appearance degrade the performance of model prediction. Moreover, it requires output from multiple models, which can be computationally expensive and affect real-time performance. Methodology: A multi-task learning (MTL) model is proposed for surgical report generation and tool-tissue interaction prediction that deals with domain shift problems. The model forms of shared feature extractor, mesh-transformer branch for captioning and graph attention branch for tool-tissue interaction prediction. The shared feature extractor employs class incremental contrastive learning (CICL) to tackle intensity shift and novel class appearance in the target domain. We design Laplacian of Gaussian (LoG) based curriculum learning into both shared and task-specific branches to enhance model learning. We incorporate a task-aware asynchronous MTL optimization technique to fine-tune the shared weights and converge both tasks optimally. Results: The proposed MTL model trained using task-aware optimization and fine-tuning techniques reported a balanced performance (BLEU score of 0.4049 for scene captioning and accuracy of 0.3508 for interaction detection) for both tasks on the target domain and performed on-par with single-task models in domain adaptation. Conclusion: The proposed multi-task model was able to adapt to domain shifts, incorporate novel instruments in the target domain, and perform tool-tissue interaction detection and report generation on par with single-task models.