Thank you for the credentials.
I have manually posted on the front-end and auto-posted articles in the backend. All posts seemed to go to the appropriate Facebook pages, so I'm a little confused at what your problem is now.
Here are the steps that I took:
1. Enabled both channels in the backend Channels area.
2. On the front end, logged in with the credentials.
3. I went to a Greek article page and used the Create Post toolbar in the bottom of the page to manually post to Facebook. (Side note, I had to use dev tools to enable the modal-footer since your template hides it and, thus, the post button). This went properly to your FB Greek Page - look for the post with the text "Test Gr bakches-apo-ten-omada-ki-omos-kineitai-sto-theatro-roes"
4. I then went to an English article page and posted manually as well. This went properly to the FB English page - look for the post with the text "Manual Post EN why-did-ancient-greek-actors-wear-theater-masks"
5. In the backend, created an article in a Greek category - article ID 17663. This posted properly to the FB Greek page - look for the post with the text "Test GR Autopost 1"
6. In the backend, created an article in an English category - article ID 17664. This posted properly to the FB English page - look for the post with the text "Test En Autopost 1".
At this point, I'm confused. Can you please explain step-by-step what problem you're having and any details like which articles (and their IDs) posted incorrectly, etc.