In data saving mode, the traffics routed through a proxy server for compression. It is likely that the web site will be able to know your actual IP address through javascript etc. For more anonymous usage, you should consider the OS level VPN.
If you want to confirm the actual IP address seen by the server, you can hit https://www.ip2location.com and see the results. If you see Opera organization, then you are behind the data saving mode in Opera Mini.