Cannot apply different robots.txt for each multi-site.

Hi,
I have successfully installed the module, I can edit the robots.txt in the UI and when I call mysite.com/robots.txt I can see the new version. Great.
But the reason why I installed it in the first place is to be able to have different robots.txt files for each one of my sites since I have a multi-site configuration and this part does not work. Whenever I make a modification from the UI of one of the sites (in different web sessions), it gets applied to all others.

This makes me wonder if I have a special multi-site config? My multi-sites are all pointing to the same Drupal / database. I only have a different theme, site name and front page for each one configured in its settings.php.
Basically I would like the robots.txt of the default site to be the regular one, and I would like to disallow all for all the other multi-sites. Is that possible ?
Thank you in advance