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Multi-agent LLM systems introduce a security risk in which sensitive information accessed by one agent can propagate through shared context and reappear in downstream outputs, even without explicit adversarial intent. We formalise this phenomenon as propagation amplification, where leakage risk increases across agent boundaries as sensitive content is repeatedly exposed to downstream generators. Existing defences, including prompt-based safeguards, static pattern matching, and LLM-as-judge filtering, are not designed for this setting: they either operate after generation, rely primarily on surface-form patterns, or add substantial latency without modelling the generation process itself. To resolve these issues, we propose PRISM, a real-time defence that treats credential leakage as a sequential risk accumulation problem during generation. At each decoding step, PRISM combines 16 signals spanning lexical, structural, information-theoretic, behavioural, and contextual features into a calibrated risk score, enabling per-token intervention through green, yellow, and red risk zones. Our central observation is that credential reproduction is often preceded by a measurable shift in generation dynamics, characterised by entropy collapse and increasing logit concentration. When combined with text-structural cues such as identifier-pattern detection, these temporal signals provide an early warning of leakage before a secret is fully reconstructed. Across a 2,000-task adversarial benchmark covering 13 attack categories and three pressure levels in a heterogeneous four-agent pipeline, PRISM achieves F1 = 0.832 with precision = 1.000 and recall = 0.712, while producing no observed leakage on our benchmark (0.0% task-level leak rate) and preserving output utility of 0.893. It substantially outperforms the strongest baseline, Span Tagger, which achieves F1 = 0.719 with a 15.0% task-level leak rate.