This plugin is great and is really close to what I needed. I did have to modify it a little bit to make it work. The current plugin uses dynamic_sidebar() function which is outputting content outside of your $value variable and isn’t returned with the function.
By adding ob_start() and ob_get_contents you can save this output and return it properly within your div. (If you look now, the <div id=”secondary”> gets displayed after the sidebar)
Here is the final code change to make this work so that ACF functions get_field (returns the html) and the_field (displays the html) work properly.
<br />
function format_value_for_api($value, $post_id, $field)<br />
{<br />
$value = '';<br />
if ( is_active_sidebar( $field['value'] ) ) :<br />
$value .= '<div id="secondary" class="widget-area" role="complementary">';<br />
ob_start();<br />
dynamic_sidebar( $field['value'] );<br />
$value .= ob_get_contents();<br />
ob_end_clean();<br />
$value .= '</div><!-- #secondary -->';<br />
endif;<br />
return $value;<br />
}<br />
https://wordpress.org/plugins/advanced-custom-fields-widget-area-field/