Update DropDownChoice in DataView

I made a download page in Wicket. As you can see, it's a DataView where you can download a file, depending on the id column and the DropDownChoice 'version'.

So clicking 'Download' on id 160 with version 3 should download file160ver3.txt, while on id 159 with version 2 it should download file159ver2.txt. Unfortunately updating the DropDownChoice doesn't get reflected in the model. So clicking on the Download button always downloads the file in the same version. As I have defaulted to Version 2 in my DropDownChoice, it always downloads this version.

Here's my code:

DropDownChoice<Integer> choice = new DropDownChoice<>("version", new Model<Integer>(2), List.of(1, 2, 3));
choice.add(new AjaxEventBehavior("change") {
    @Override
    protected void onEvent(AjaxRequestTarget target) {
        target.add();
        System.out.println(choice.getModelObject());    // doesn't change
    }
});
item.add(choice);

// The value of choice.getModelObject() doesn't change
DownloadLink download = new DownloadLink("download", getFile(p.getId(), choice.getModelObject()));
download.setOutputMarkupId(true);
item.add(download);

What is it that I'm missing? How do I update the DropDownChoice?

Update and solution (changed according to Svens suggestion):

        choice.add(new AjaxFormComponentUpdatingBehavior("change") {
            @Override
            protected void onUpdate(AjaxRequestTarget target) {
                System.out.println(choice.getModelObject());
            }
        });
        item.add(choice);

        DownloadLink download = new DownloadLink("download", () -> {
            return getFile(p.getId(), choice.getModelObject());
        });

        // ...

private File getFile(int id, DropDownChoice<Integer> choice) throws FileNotFoundException, IOException {
    Integer version = choice.getModelObject();

Thanks.

... And here's the complete code (Java and HTML below):

public DownloadPage(PageParameters params) {
    List<PrefKey> prefKeys = db.getPrefKeys();
    DataView<PrefKey> dataView = getDataView(prefKeys);
    Form<Void> form = new Form<>("form");
    add(form);
    form.add(dataView);
}

private DataView<PrefKey> getDataView(List<PrefKey> prefKeys) {
    IDataProvider<PrefKey> provider = new ListDataProvider<>(prefKeys);
    DataView<PrefKey> dataView = new DataView<>("dbAsDataView", provider, 10) {
        private static final long serialVersionUID = 12345L;

        @Override
        protected void populateItem(Item<PrefKey> item) {
            PrefKey p = item.getModelObject();
            item.add(new Label("tdId", p.getId()));
            item.add(new Label("tdKey", p.getKey()));
            try {
                DropDownChoice<Integer> choice = new DropDownChoice<>("version", new Model<Integer>(2), List.of(1, 2, 3));
                choice.add(new AjaxEventBehavior("change") {
                    @Override
                    protected void onEvent(AjaxRequestTarget target) {
                        target.add();
                        System.out.println(choice.getModelObject());    // doesn't change
                    }
                });
                item.add(choice);

                DownloadLink download;
                // The value of choice.getModelObject() doesn't change
                download = new DownloadLink("download", getFile(p.getId(), choice.getModelObject()));
                download.setOutputMarkupId(true);
                item.add(download);
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    };
    return dataView;
}

    <h1>Wicket Download</h1>
    <form wicket:id="form" action="">
        <table id="tblDataView" class="table table-striped table-hover">
            <thead>
                <tr>
                    <th>Id</th>
                    <th>Key</th>
                    <th>Version</th>
                    <th>Download</th>
                </tr>
            </thead>
            <tbody>
                <tr wicket:id="dbAsDataView">
                    <td wicket:id="tdId"></td>
                    <td wicket:id="tdKey"></td>
                    <td><select wicket:id="version"></select></td>
                    <td><input type="button" wicket:id="download" value="Download"></input></td>
                </tr>
            </tbody>
        </table>
    </form>