The emerging paradigm of embodied intelligence, which emphasizes the tight coupling between physical embodiment and cognitive processes, has opened up new frontiers in Human-Computer Interaction (HCI), particularly for smart personalized exercise monitoring. Despite its significant potential, existing systems often struggle in multi-user environments, where the accuracy and reliability of exercise tracking are severely compromised by the complexity of human behaviors and interactions. To address this critical issue, this paper proposes a multimodal fusion framework that integrates Radio Frequency Identification (RFID) and Computer Vision (CV) technologies for personalized exercise monitoring in multi-user scenarios, which is the first work to enhance interaction-aware perception in such settings. The system workflow consists of three core modules: Data acquisition, perception modeling, and exercise monitoring, which collectively enable comprehensive analysis of individual exercise behaviors. The system leverages multimodal data from RFID tags and a depth camera to jointly identify object ownership and recognize user activities in real time. Extensive experimental results demonstrate that the proposed system achieves an average matching accuracy of 95%, and an average estimation accuracy of 94%.