Answer
Aurena custom field translations need to be entered separately from the EE Custom Field Translation entries — they aren't shared automatically. After adding the custom field to a page via Aurena Page Designer and publishing that page, a new corresponding entry appears in Text Translations; you need to add the same translation text there as well, matching what you originally entered for the EE Custom Field Translation. Note the entry's Path in Text Translations includes a context prefix (for example, '[global]' if the field was added to the Global context) — each context maintains its own separate translation, so make sure you're editing the translation under the correct context. After entering the Aurena-side translation and refreshing the language cache, you may also need to unpublish and republish the page in Page Designer for the field to actually pick up its proper translation.