How can I make changes at my side, to allow the old url still working, without send a redirect to client side and ask their browser redirect to new link (in a single request and response)? Because bandwidth and time is a concern. Can I make it at my server side?
Yes, you can, assuming you are allowed to put htaccess files on your server. You can have all non-existent files (like admin/login.php) rerouted to your Yii entry script without redirecting browsers.
Please look at the bundled htaccess file in your downloaded Yii package.