Well, without any information I can’t really do much.
It seems to me. I was only interested on how the translations actually worked. From the site front-end it looks like it is some sort of an on-the-fly translation based on the URL, using a cache or something similar.
I was hoping they have an application hook (possibly a filter or a function call), which could be applied to the ajax call, with the language variable to transform the results, but I guess it is not possible.