Weird bug : old version of mobile site showing

I have a very annoying problem and I can not understand it, it is simply beyond all logic.

Let me explain :

I had an online site with a custom responsive theme that I was changing, everything seemed to work, except that I realized that viewing my site from a mobile, the page displayed was old and not updated (new articles not visible, old widgets etc.). All changes are however visible on conventional computer.

I tried to remove the cache from my mobile, no effect. Cookies, no effect. I tested on a tablet: same problem, an older version appears. I tried from a friend’s phone, same problem.

I told myself that this might be a problem with the WordPress installation, so I deleted everything and reinstalled it on the ftp.

Suprise: The site still displays an old version on mobile, but not on computer.

The weird part: source files DO NOT EXIST MORE on my ftp, so how is it possible that the old site is still displayed ?

I tried to empty the cache from my server provider. NO EFFECT.

When testing my website on google mobile test :

https://www.google.com/webmasters/tools/mobile-friendly/?url=www.salutparis.fr

The old theme appear : yellow logo and yellow interface

When testing from a computer :

https://www.salutparis.fr New theme appear : twenty fifteen

You can try from your own mobile, it will display a yellow interface : OLD VERSION.

Can someone explain to me what’s going on?

Thank you !