Your translations are safe
Built-in support for translating content into multiple language was only introduced in Joomla! in version 1.6. Before that, we had to use 3rd-party extensions, the most famous being Joomfish. Using such tools has proved very useful, if not essentials, in those times, but that came with a price: vendor lock-in.
Most third-party multilingual extensions store translated content in their own database table, under their own format. And when times come to update Joomla! to a newer version - for instance from Joomla! 1.5 to Joomla! 2, or even to Joomla! 3, we have seen many people locked up, having to wait months until the extension they use has been updated. And sometimes that update never happened.
All translations managed by Josetta are regular Joomla! content. Your content and your translations are future-proof, as updating from one Joomla! major version to the next will always be possible. To measure how safe you are, you can uninstall Josetta entirely: your site will continue displaying just as before, original content and translations.
Just don't forget to install it back again, your translators will miss it ;)