Shouldn't the translated taxonomy terms get automatically chosen in all languages?

Hello.

I have a site whose default language is French and other enabled languages are English, Mongolian and Italian. The idea is to have the interface in Mongolian, with a fallback into French for strings not translated into Mongolian, and the content will be in French, with some parts translated into English and Italian.

Views and Internationalization modules are enabled. The language detection and selection is set to user, browser and default, in this order. I have one vocabulary, called "type". In the list of its terms, all versions of all terms appear. If I edit, for instance, the English term "Hiking &Trekking", and go to the tab "Translate", I get its French version "randonnée pédestre" and its Mongolian version: "явган аялал". I have a content type called "voyage" with a "Term reference" field labelled "аяллын төрөл", named "fields_tags". If I edit it, its vocabulary is "Type" and all the versions of the taxonomy terms are listed as possible "default value"-s, including "Hiking &Trekking", "randonnée pédestre" and "явган аялал", though I've chosen no default value. I have a content of type "voyage" and of French language called "La fameuse vallée Orkhon et le lac Naiman". It has not been translated so far. If I edit it in Mongolian, its field "аяллын төрөл" is set as "явган аялал" (the list of possible fields is the list of Mongolian taxonomy terms). But if I edit it in French or in English, changing the user language to do so, thene the checkboxes "Hiking &Trekking" or "randonnée pédestre", respectively, appear unchecked, in the list of English or French (respectively) taxonomy terms.

What I would expect is that, once a taxonomy term as been chosen for a given content, the different versions of the term get automatically chosen in all languages, and appear according to the interface language detection and selection method.

Is this a bug, or do I miss something?