Nginx Reverse Proxy to LAMP server : can’t login to phptheadmin

I'm quite new to apache and even newer to reverse proxy, but I ended up installing a server with nginx (as a reverse proxy) and apache, to manage websites with different technologies. A php website (called php_site below) is handled by apache, a ruby on rails website is handled by nginx. More websites should be added later. Everything's working fine, except for phpmyadmin.

My problem : I can get to phpmyadmin login page (either through www.php_site.org/phpmyadmin/ or xx.xx.xx.xxx:8080/phpmyadmin/, xx being my server external IP), but I don't manage to log in. I'm pretty sure I have the good credentials, but when I submit the form, phpmyadmin login page simply reloads, without displaying errors.

My conf :

• ubuntu 16.04
• php 5.6 (because an old project needed it)
• phpmyadmin 4.5.4.1
• mysql 5.7.17
• Apache/2.4.18

phpmyadmin is installed in /usr/share/phpmyadmin/.

Nginx conf (php_site) :

# /opt/nginx/conf/conf.d/php_site.conf 
server {
  listen 80;
  server_name www.php_site.org;

  location / {
    proxy_pass http://127.0.0.1:8080;
    proxy_set_header Host $host;
    proxy_set_header X-Real-IP $remote_addr;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header X-Forwarded-Proto $scheme;
  }

  location /phpmyadmin {
    proxy_pass http://127.0.0.1:8080/phpmyadmin;
    proxy_set_header Host $host;
    proxy_set_header X-Real-IP $remote_addr;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header X-Forwarded-Proto $scheme;
  }

 client_max_body_size 15M;

}

server {
    listen 80;
    server_name php_site.org;
    rewrite ^ http://www.php_site.org$request_uri? permanent;
}

Apache conf (php_site) :

# /etc/apache2/sites-available/php_site.conf
NameVirtualHost  *:8080

<VirtualHost *:8080>

  ServerName www.php_site.org
  ServerAdmin myself@mail.com
  DocumentRoot /var/www/php_site.com/htdocs


  <Directory /var/www/php_site.com/htdocs >
    AllowOverride All
    DirectoryIndex index.php
  </Directory>

  ErrorLog /var/log/apache2/php_site-error.log

  LogLevel warn

  CustomLog /var/log/apache2/php_site.log combined

</VirtualHost>

<VirtualHost *:8080>
    ServerName php_site.org
    Redirect permanent / http://www.php_site.org/
</VirtualHost>

Questions :

• is there something wrong with my conf ?
• do I need to set $cfg['PmaAbsoluteUri'] in /etc/phpmyadmin/config.inc.php ? And if yes, what is the correct value ? (cf https://docs.phpmyadmin.net/en/latest/faq.html#faq4-7) (I trid many with no success)
• would it be better if I didn't proxy_pass php_my_admin ? (and manage instead to do something like http://www.jaredlog.com/?p=2117, even if my configuration is different ?)

Don't hesitate to ask fo further info if needed.