Content Targeting with User Segments just works with Content Search Web Parts but some additional work is needed if you want to leverage it with the Search REST API.
Leveraging SharePoint 2013 Search REST API for anonymous users allows you to build powerful search-driven solutions. Often, particularly in the early stages of the project, queries might not work as expected. So how do you find out what’s wrong?
Leveraging the Search REST API allows you to build rich search-driven solutions. If you’re not careful however, you might get results other than intended even though everything seems to be working correctly.
SharePoint 2013 offers rich API for interacting with Managed Navigation. Unfortunately, some additional work is required if you need to use it with anonymous users.
Granting the “Retrieve People Data for Search Crawlers” administration permission on the User Profile Service Application using PowerShell
When working with search-driven solutions, or even if you just want to be able to search for people, SharePoint Search has to be granted access to that information in order to crawl it. Generally all of this is being automatically taken care of when provisioning the Search Service Application. On rare occasions you might however need to grant this permission manually.