Relevanssi generally works well with Ultimate Member and can be used to search Ultimate Member profiles. Ultimate Member doesn’t do custom profiles but instead builds upon WordPress user profiles.
If you want to change the default /author/ URLs for user profiles in search results to point to the /user/ URLs Ultimate Member uses, that’s easy to do with the relevanssi_user_profile_to_post filter hook. Add this to your site:
add_filter( 'relevanssi_user_profile_to_post', 'rlv_ultimate_member' );
/**
* Filters the user profiles when Relevanssi converts them to posts.
*
* @param object $post The post object (not a WP_Post object!).
*
* @return object The filtered post.
*/
function rlv_ultimate_member( $post ) {
$post->relevanssi_link = str_replace( '/author/', '/user/', $post->relevanssi_link );
return $post;
}