Safari Private Browsing is saving User Names

Launch the Keychain Access application and enter "facebook" (without the quotes) in the search box. Delete any keychain items listed. If you're later prompted to save a password in the Keychain, click Never.

If this is your computer, you should create separate user accounts for all regular users, and/or activate the Guest account. If it's not your computer, you should have no expectation of privacy when using it.

I tried what you said with keychain access, but facebook never popped up

Either All Items or Passwords must be selected in the list at lower left. If it was, then Safari may be autofilling the login fields from information cached in memory. When private browsing is deactivated, that information should be erased.

Select Safari > Preferences > Privacy from the menu bar and click Details. If there are any cookies from Facebook, delete them. Close the preferences window, then open it and check again. Are the cookies still gone?

Quit the application if it's running. Triple-click the line below to select it:

~/Library/Cookies/Cookies.binarycookies

Right-click or control-click the highlighted line and select Services ▹ Reveal from the contextual menu. A Finder window should open with a file selected. Move the selected file to the Desktop, leaving the window open. Relaunch the application and test. If there's no change, quit again and put the file you moved back where it was, overwriting the one that may have been created in its place. Otherwise, delete the file you moved.

~/Library/Caches/com.apple.Safari

Did you completely reset Safari?

Also delete the Flash cache:

~/Library/Caches/Adobe/Flash Player

If that doesn't work, proceed as follows.

Read this whole message before doing anything.

Back up all data.

Quit Safari if it’s running. Then select  ▹ Force Quit... from the menu bar. A small window will open with a list of running applications. Safari may appear in that list, even though you quit it. If so, select it and press return. Close the window.

Step 1

Hold down the option key and select Go ▹ Library from the Finder menu bar. Delete the following items from the Library folder (some may not exist):

Caches/com.apple.Safari

Caches/com.apple.WebKit.PluginProcess

Caches/Metadata/Safari

Preferences/com.apple.WebKit.PluginHost.plist

Preferences/com.apple.WebKit.PluginProcess.plist

Saved Application State/com.apple.Safari.savedState

Leave the Library folder open. Try Safari again. If it works now, stop here. Close the Library folder.

Step 2

If you still have problems, quit Safari again.

Launch the Terminal application in any of the following ways:

☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)

☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.

☞ Open LaunchPad. Click Utilities, then Terminal in the icon grid.

Drag or copy — do not type — the following line into the Terminal window, then press return:

rm -fr $TMPDIR../C/com.apple.Safari

Quit Terminal. Launch Safari and test.

Step 3

If Safari still doesn’t work right, quit, go back to the Finder and move the following items from the open Library folder to the Desktop (some may not exist):

Cookies/Cookies.binarycookies

Preferences/com.apple.Safari.LSSharedFileList.plist

Preferences/com.apple.Safari.plist

Preferences/com.apple.Safari.RSS.plist

Preferences/com.apple.WebFoundation.plist

PubSub/Database

Safari

(Note: you are not moving the Safari application. You’re moving a folder named “Safari.”)

Try again. This time Safari should perform normally, but your settings and bookmarks will be lost.

If the issue is still not resolved, quit Safari again and put all the items you moved to the Desktop back where they were, overwriting the newer ones that will have been created in their place. You don’t need to replace the files you deleted in step 1. Stop here and post again.

If Safari is now working normally (apart from the lost settings), look inside the “Safari” folder on the Desktop for a file named “Bookmarks.plist”. Select File ▹ Import Bookmarks from the Safari menu bar. Import from that file. Recreate the rest of your Safari settings. You can then delete the items you moved to the Desktop.

Note: This step will remove your Safari Extensions, if any, and their settings. If you choose to restore them, do so one at a time, testing after each step to make sure you haven’t restored the problem.

If you don’t like the results of step 3, you can undo it completely by quitting Safari and restoring the items you moved or deleted in that step from your backup, overwriting any that were created in their place.

I don't have any other suggestions. I can't explain what you say is happening. I repeat that you should not expect privacy when sharing an account with others or using a computer you don't control.