Cloud environments built on Amazon Web Services face a structural security vulnerability: once a credential passes authentication, the resulting session is often treated as trusted for its entire duration. This assumption fails when credentials are stolen. We introduce the Explainable Adaptive Zero Trust Framework (EAZTF), a cloud-native security layer that continuously reevaluates the legitimacy of API actions throughout a session. EAZTF combines Isolation Forest and XGBoost to evaluate eight CloudTrail and IAM-derived behavioral features in real time and produce a Trust Risk Score (TRS) that determines whether a session continues, requires step-up MFA, or is restricted. Each decision is accompanied by a SHAP or LIME explanation, providing human-readable audit records for security analysis and compliance. The framework is also evaluated against four adversarial evasion strategies: credential theft, behavioral mimicry, API rate evasion, and privilege escalation. Experiments on an 8,500-record synthetic CloudTrail dataset show that Isolation Forest achieves 94.4% precision, 91.2% recall, and an F1 score of 0.928. Across the four adversarial scenarios, the mean detection rate is 91.0%, with behavioral mimicry being the most difficult at 83.9%. SHAP analysis identifies IP reputation, login-time deviation, and API call velocity as the three dominant features. A structured NIST SP 800-207 self-assessment gives EAZTF a mean compliance score of 93%, compared with 38% for a traditional perimeter baseline. Mean time to detect decreases from hours to under one minute. Because the evaluation uses synthetic data, these results should be interpreted as indicative rather than validated production performance.