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Remote patient monitoring (RPM) via smart consumer electronics is revolutionizing post-discharge and chronic disease management. Yet, current AI-powered RPM systems often lack transparency, adaptability across diverse devices, and integration into clinical triage systems. To address this, we introduce TeleXAI-R, an explainable AI-driven risk stratification model that operates in real-time across IoT-integrated consumer devices such as pulse oximeters, blood pressure monitors, and smart rings. TeleXAI-R incorporates a transformer-based temporal encoder for dynamic vital sign prediction and an XAI attention module that visualizes feature importance over time. We develop a cloud-edge hybrid inference engine to enable on-device alerts and clinician dashboards. The model also includes a confidence-aware alerting system to reduce false positives in high-noise settings. Core contributions include: (1) a temporal interpretability framework tailored for RPM; (2) cross-device calibration and data standardization protocol; and (3) integration with FHIR-compatible clinical workflows. Experiments on a real-world dataset of 1,200 patients show 90.1% precision in early risk detection for cardiac events, while maintaining interpretability that clinicians rated 4.7/5 in a usability study. TeleXAI-R sets the foundation for trustworthy RPM in connected healthcare. Unlike prior temporal-attention pipelines, TeleXAI-R couples a rhythm-aware transformer with a calibrated, device-agnostic alignment layer and a confidence-adaptive alerting mechanism that jointly optimize latency, interpretability, and false alerts. Removing any of these core components leads to significant drops in precision and F1, underscoring their necessity.