Alias using Nginx causing phpMyAdmin login endless loop

I had the exact same problem. I ran a website with a doc root in /var/www/somesite and wanted to hook phpmyadmin to some sub-folder on the site. I tried this with this config in nginx:

root /var/www/somesite;

location /pma/ {
    alias /usr/share/phpmyadmin/;
}

location ~ ^/pma/(.+\.php)$ {
    alias /usr/share/phpmyadmin/$1;
    fastcgi_pass   unix:/tmp/phpfpm.sock;
    fastcgi_index  index.php;
    fastcgi_param  SCRIPT_FILENAME  $request_filename;
    include fastcgi_params;
}

This seemed to work, except when I logged in, like you described, I just saw the front page again. No errors, nothing. If I logged in with a bad password, I got a "Cannot login to MySQL server"-error, as you'd expect.

Solution
Finally what I did was I dragged in all the stuff from fastcgi_params and found that changing the DOCUMENT_ROOT-parameter fixed this. So the nginx-config above changed to:

root /var/www/somesite;

location /pma/ {
    alias /usr/share/phpmyadmin/;
}

location ~ ^/pma/(.+\.php)$ {
    alias /usr/share/phpmyadmin/$1;
    fastcgi_pass   unix:/tmp/phpfpm.sock;
    fastcgi_index  index.php;
    fastcgi_param  SCRIPT_FILENAME  $request_filename;

    # From fastcgi_params
    fastcgi_param  QUERY_STRING       $query_string;
    fastcgi_param  REQUEST_METHOD     $request_method;
    fastcgi_param  CONTENT_TYPE       $content_type;
    fastcgi_param  CONTENT_LENGTH     $content_length;
    fastcgi_param  SCRIPT_NAME        $fastcgi_script_name;
    fastcgi_param  REQUEST_URI        $request_uri;
    fastcgi_param  DOCUMENT_URI       $document_uri;
    fastcgi_param  DOCUMENT_ROOT      /usr/share/phpmyadmin; # <-- Changed
    fastcgi_param  SERVER_PROTOCOL    $server_protocol;
    fastcgi_param  GATEWAY_INTERFACE  CGI/1.1;
    fastcgi_param  SERVER_SOFTWARE    nginx/$nginx_version;
    fastcgi_param  REMOTE_ADDR        $remote_addr;
    fastcgi_param  REMOTE_PORT        $remote_port;
    fastcgi_param  SERVER_ADDR        $server_addr;
    fastcgi_param  SERVER_PORT        $server_port;
    fastcgi_param  SERVER_NAME        $server_name;
    fastcgi_param  REDIRECT_STATUS    200;
}

(Side note: I think this a problem with nginx, that you can't set an alias and the doc root at the same time. Weird, actually.)

This is my config:

location /phpmyadmin {
    alias   /usr/share/phpmyadmin;
    index index.php;
    location ~ /([^/]+\.php)$ {
        try_files /$1 =404;
        fastcgi_pass unix:/var/run/php/php7.1-fpm.sock;
        fastcgi_index index.php;
        include fastcgi_params;
        fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
        location ~ /phpmyadmin/js/([^/]+\.php)$ {
            try_files /phpmyadmin/js/$1 =404;
            fastcgi_pass unix:/var/run/php/php7.1-fpm.sock;
            fastcgi_index index.php;
            include fastcgi_params;
            fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
        }
    }
}