How to check if a specific page uses a page template?

Page template is set in a post meta field keyed '_wp_page_template' so, instead of using raw $wpdb query, you can run a WP_Query using 'author' argument and meta_query to retrieve pages from a specific author that also have a specific templates:

$q = new WP_Query( array(
  'author' => $user->ID,
  'post_type' => 'page',
  'meta_query' => array( array('key' => '_wp_page_template', 'value' => 'blog.php') )
) );

if ( $q->found_posts > 0 ) {
  foreach ( $q->posts as $post ) {
    // all pages returned have the template `'blog.php'`
    wp_set_post_terms( $post->ID, $tag, $taxonomy );
    $permalink_n = get_permalink($post);
    set_cimyFieldValue( $user->ID, 'HOMEPAGE', $permalink_n );
  }
}

If you want retrieve all pages from an author, but do something for all pages and something else only for some other pages you can

$q = new WP_Query( array(
  'author' => $user->ID,
  'post_type' => 'page'
) );

if ( $q->found_posts > 0 ) {
  foreach ( $q->posts as $post ) {

    wp_set_post_terms( $post->ID, $tag, $taxonomy );

    $template = get_post_meta( $post->ID, '_wp_page_template', true );

    if ( $template === 'blog.php' ) {
      $permalink_n = get_permalink($post);
      set_cimyFieldValue( $user->ID, 'HOMEPAGE', $permalink_n );
    }

  }
}