For instance, if I attach pdf file. Firstly, when I logged in, it shows fake address briefly at the beginning, but final page, it shows the actual address.
When you are logged in and you take a look at your normal blog page then all links you will see are the real, the right links to the media files (e.g. .mp3 or .pdf files). But if you are using the statistic feature of podPress then all links will getting masked. For instance: http://example.com/wp-content/uploads/2010/10/hello.mp3 becomes http://localhost/wp30mu/podpress_trac/web/123/0/hello.mp3. If you click on such a link and it is e.g. a .pdf file then podPress counts with the help of this special URL schema the download and hands the browser the original URL and when your browser shows the .pdf in the browser windows itself (and does not show you a download dialogue) then you will see the complete URL in the address bar of your browser.
Is that what you have observed?
The URL masking of the statistic funtion has nothing to do with the fake enclosure.
The so called fake enclosure are only visible if you use a feed reader to view e.g. the RSS feed of your blog. If you are not logged in then the feed reader will show instead of the real media file a place-holder file with the name podPress_Protected_Content.mp3 independently of the type of the real file (instead of e.g. mypremium.pdf it will podPress_Protected_Content.mp3, too). Furthermore the URL of such a fake enclosure will be different from the real URL, too. If someone has not the rights to read, listen or watch the premium files, he has at least to guess the location of the files. But as the description of the premium feature says: "Keep in mind, that this does NOT protect your content if someone discovers the URLs, it only hides the location from showing up on the site or in the feed. To fully protect your files you can use this feature in combination with an external service [...]"
If a feed has no enclosures then iTunes and other feed readers will not show enclosures. But if a feed includes at least fake enclosures then e.g. iTunes will show at least them. In other words if there no enclosures iTunes shows no new "episodes". If you are not using fake enclosures then the default RSS feed of your blog contains the posts of the premium content but without enclosures. That may be no problem but all subscribers which are using e.g. only iTunes to follow your blog will not get noticed of new posts resp. episodes (if there are no enclosures in the posts in the feed). The point of having fake enclosure is to show that a post contains an media file.
Enclosures are special elements (not only) of RSS feeds (http://en.wikipedia.org/wiki/RSS_enclosure). They contain an URL usually to a media file, the size (in Byte) and the type of the media file. The fake enclosures which podPress creates are like that but with modified URLs.
If you want to protect your files better then you could use external services or if you are not afraid of technical things then you could put your premium files in different folders which you can be protected with passwords. One way to protect folders on Apache webserver with passwords is to use .htaccess and .htpasswd files. Such a login would be independently from the blog login (but you could use the same login names and passwords). I'm no an expert for this technique but you can find many guides and How-Tos if you search the Internet e.g. for "password protection htaccess".
is there any way to search the posts with premium contents?
You mean tell the internal blog search "give me all posts with premium content"?
Maybe. If the content or titles of these posts have a special string like e.g. "Premium" or if the posts with premium files are in a special category or if they have same tags then you can find them.
Or if you want to retrieve the IDs of posts with premium content then the SQL query string could look like this:
SELECT DISTINCT post_id FROM wp_postmeta WHERE meta_key = 'podPressMedia' AND INSTR(meta_value, 'premium_content')