Thanks for the tip!
I was editing the content & translations in the multiple tabs/windows. I have open the same document in multiple languages in different tabs/windows and then I was checking the content between translations/windows.
The reason I was doing this is because the Propulsion theme (Avia framework) data was not copied between translations - despite that I used the WPML Translation "duplicate" option. So the "Featured media" gallery, slideshow & layout data didn't make it to the translations and I had to copy & check the data between different translations.
The admin page language (dropdown at the top) and Language in the sidebar was shown correctly.
All the NON Propulsion theme (Avia framework) data was saved correctly!
The solution to my problem was to NOT to have opened multiple tabs/windows in different languages.
Probably manually selecting already correctly selected language from the admin dropdown would do the trick to.
I think there are two bugs here:
1.) Propulsion theme (Avia framework) data is not copied over to translations when using WPML Translation "duplicate" option.
2.) The Propulsion theme (Avia framework) data is not saved when you have open multi tabs/windows with different languages. At the same time all other "native" WP content is saved without any problem.
It would be great if at least one of those problems could be fixed.
Please let me know if I can look forward for patch that would solved the issue.
Thank you for your help and pointing me in the right direction.