Found where it came from, my bad:
1/ I had not noticed the output of /etc/rc.tini was redirected to
"uncaught-logs" so I could not properly check it was executed or not.
2/ I tried to unmount all filesystems during the shutdown of s6-rc, which fails
because the root cannot be unmounted at time, causing the shutdown to fail.
Now that I redirected the output to the console and moved unmounting and
process killing into /etc/rc.shutdown, everything seems to go fine.