Toad checks scores on every check-in and compares them to the scores on the last check in. If the scores are lower than the last check-in, then it will result in a validation failure. By default, these metric values are stored in your local user files to be used for comparison with the current check-in. Only the last set of values are saved for each object . So this is a client-based setup and comparisons can only be run for a single user. If user A checks something in and metrics are stored, user B won't have these metrics to compare against, if he/she checks in the same object. This is where 'Store check-in metrics on the server' comes in to play. If store on server is checked, then User B's check-in metrics can get compared to user A's previous check-in metrics.
The Code Analysis values that are displayed to the user in Report | Code Analysis Metrics History, are only triggered by the main Code Analysis option to 'Save results to DB' from the CA module itself. The Team Coding option to "store check-in metrics on server" only keeps metrics stored as a basis for a comparison and are only displayed if a validation error occurs due to lower scores.