Ok, now i understand. The browser sends a request withe the if-not-modified-since corresponding to one server to the other server, and this one reply with 200 since the mtime is in the future of the if-not-modified-since

is there any simple solution to handle this? I don't want to rsync assets between the servers

I use django in my project and its static/collectstatic process. So, i force the mtime of each static file collected, afet each collecstatic operation. I give the command line if someone fall in the same trap:
./manage.py collectstatic --noinput && find static -type f -exec touch -t $(date +%m%d%H)00 '{}' \;

Now, the cache is working as intended and my servers are in active-active setup.

Thanks for your answer that leads me to the solution