INC Permission

After installation, isn't the folder 'inc' permission supposed to change to 555?

No. You as the account owner needs to have write permissions so the FTP account and cPanel account can still write to it. So the proper permissions for the inc folder is 755.

Removing write permissions for the owner is the number one reason why most upgrades to newer versions of dolphin fail. Without write permissions by the owner of the FTP account to the inc folder will prevent the uploads of replacement files during the upgrade resulting in a incomplete upgrade.

Dolphin when run under CGI/FastCGI expects it to be 555 after installation. As Deano said, 755 is fine and has the least issues when using FTP or editing anything in there - there's  skip button on the installer for a reason.