Term labels not localized

I did some further debugging by installing vanilla Drupal and minimum required modules, only search_api_et is in dev state. In the listing, the terms always appear in their source language, exposed filters and non-search_api views show everything as I expect.

Bumping up to major to get some attention!

I think the problem is in search_api because it's storing the name of the taxonomy term when it is chosen to be indexed instead of storing term ID (tid) which is more useful and can be used to get the term name in the user's language.

I came up with a quite ugly workaround using Views PHP module and processing the term ID with some php:

<?php
global $language;
$term_ids = array();
$term_ids = $data->_entity_properties['FIELD_MACHINE_NAME'];
$terms_localized = array();
foreach($term_ids as $term_id) {
  $term = taxonomy_term_load($term_id);
  // Reading localized terms using term id
  $terms_localized[] = i18n_taxonomy_term_name($term, $language->language);
}
print(implode(", ", $terms_localized));
?>

Notice that this snippet uses the i18n_taxonomy_term_name() function from i18n module.

So you include the taxonomy term field you need in the view and exclude it from display, then adding a PHP field with the snippet above will print the term in localized form.