Not sure if this is the place to report bugs, but didn't find any better, so here I am.
In the script /etc/openvpn/auth-pam.sh, there are the following lines.
ovpn_inst=$(echo $config | sed 's/openvpn-//g' | sed 's/.conf//g')
auth_file="/etc/openvpn/auth_$ovpn_inst"
As $config points to the full path of the config file, the result of the consecutive sed invocations is that ovpn_inst becomes equal to /var/etc/<name of the openvpn config>.
As a result auth file assumes the value of /etc/openvpn/auth_/var/etc/home_vpn. At a later point the script checks if the file pointed by $auth_file exists and naturally /etc/openvpn/auth_/var/etc/<name of the openvpn config> does not exist, so it's impossible to authenticate with the TLS/Password method.
If the sed statements get fixed everything works fine.