Affiliation when submitting a revised paper I recently started (last week) a post-doc position and I have a submitted paper which got an R&amp;R  before finishing my Ph.D and having this post-doc position. 
I will resubmit the paper this week and my current director says that I should change the affiliation on the revised version of the paper and mention that the paper is financially supported by the institution where I am a post-doctoral fellow.

I wonder if it is correct and ethical to change the affiliation because 99,9% of the work has been done under the financial support of the institution where I have done my Ph.D.
Affiliation is mostly for identification. There is no formal definition requiring it to be linked to the institution in which most of the work was done. I'd suggest that you follow the advice of your director, for political reasons if no other. It may be important to the current institution to connect itself to your work. 

But there is no reason that you can't also acknowledge your former institution within the paper if they also gave you support. Add a footnote mentioning the institutions that supported the work.