What time period does AWS anomaly detection train on?

Check out our user guide for Amazon CloudWatch Anomaly Detection. It mentions

After you create an alarm, you can adjust the anomaly detection model. You can exclude certain time periods from being used in the model creation. It is critical that you exclude unusual events such as system outages, deployments, and holidays from the training data. You can also specify whether to adjust the model for Daylight Savings Time changes.

As for your band narrowing after a week or so, the band represents the expected "normal" range for the metric values. Check out this Knowledge Center article that dives a bit more into that. Here's the important section:

After you create a model, CloudWatch anomaly detection continually evaluates the model and makes adjustments. It does this to make sure that its analysis is as accurate as possible. If another anomaly detection model that is trained with the most recent data performs better than the current model, then CloudWatch anomaly detection switches to the new model. This can cause the anomaly detection bands to shift

Essentially, you're training your model on data that includes unusual events. This creates a large band to account for the unusual data points. As time goes on the model is regularly retrained on current data points, which narrows the band, making your model more accurate at recognizing abnormalities. Just use data points that accurately portray what "normal" looks like and it will successfully train and retrain your model as time goes on.