The State field does not get set automatically. The intent is to indicate which Iteration is in Progress (where the team has Committed to a body of work) which Iterations are being Planned for some future work, and which Iterations have had the work Accepted. These values are set manually.
If an Iteration is in the Accepted State no additional work can be added to it, and in most cases Accepted Iterations will not show up in dropdown selectors for work items, although they can still be viewed, reported on, etc.
You could look at something like the Iteration Scope Change app to see if work is being added or removed during the Iteration, and the metrics on the Iteration Status and Team Board pages show the progress of delivered versus planned work.