Dear all,
I wanted to inform any user interested in my question, how I solved it.
As sometimes happen, I have been working on my problem the whole day before posting here, and few minutes after I open the question, I saw the light on what was happening.
Following:
https://mysiteurl.com/wp-content/blabla/blablabla.css?ver=3.4.2
File not compressed, nor minified.
Solution:
/wp-content/blabla/blablabla.css (without the version)
All this in the manual selected files for the proper delivery to the CDN.
I hope it could help if somebody else if having this problem.
Many thanks for your amazing plugin.
Daniel