Jeremy Pry

When using the <a href="http://support.wpengine.com/staging/" rel="nofollow ugc">Staging site</a> on WP Engine, you may want to prevent the staging version of your site from sending emails to your site users. This plugin redirects all emails to the site admin.
This plugin should be activated on your Production site. Don’t worry — it won’t do anything unless it is active on Staging site. Once you create a new copy of your Staging site, the plugin will start taking effect there.
This plugin is compatible with WordPress Multisite. If you’re using it in a Multisite environment, it is recommended to either Network Activate the plugin, or follow the instructions for installing it to the <code>mu-plugins</code> directory.

Redirect Emails on Staging

Redirect any emails that are sent by the staging site to the administrator of the site.

LeanPlugins

This plugin requires you use WPengine.com hosting. This plugin is not developed, endorsed or supported by WPengine.com.
Lean WP Engine Staging Theme will change the color of your admin bar add striped bars at the top and bottom of the admin sidebar and add STAGING text to the admin bar when you are using your staging site on WPengine. This will help alert you visually that you are on the STAGING site. This is helpful if you have both the STAGING and Production sites open at the same time in different browsers or tabs.

Lean WP Engine Staging Theme

Requires you use WPengine.com hosting. Plugin will change your admin bars to visually alert you that you are on a WPengine staging site.

Redirect Emails on Staging vs Lean WP Engine Staging Theme