Previous research on behavior-based attack detection for networks of IoT devices has resulted in machine learning models whose ability to adapt to unseen data is limited and often not demonstrated. This paper presents IoTGeM, an approach for modeling IoT network attacks that focuses on generalizability, yet also leads to better detection and performance. We first introduce an improved rolling window approach for feature extraction. To reduce overfitting, we then apply a multi-step feature selection process where a Genetic Algorithm (GA) is uniquely guided by exogenous feedback from a separate, independent dataset. To prevent common data leaks that have limited previous models, we build and test our models using strictly isolated train and test datasets. The resulting models are rigorously evaluated using a diverse portfolio of machine learning algorithms and datasets. Our window-based models demonstrate superior generalization compared to traditional flow-based models, particularly when tested on unseen datasets. On these stringent, cross-dataset tests, IoTGeM achieves F1 scores of 99\% for ACK, HTTP, SYN, MHD, and PS attacks, as well as a 94\% F1 score for UDP attacks. Finally, we build confidence in the models by using the SHAP (SHapley Additive exPlanations) explainable AI technique, allowing us to identify the specific features that underlie the accurate detection of attacks.