This is the first time I encountered similar thing. When I log into the Twitter web site in Chrome (namely, the Iron version which is said to be security enhanced, but that does not matter here) in private browsing mode it automatically logs me into my Twitter account in the main browser window as well.

• Is it a feature of Twitter?
• Or a bug of Chrome?

This can be very embarrassing, indeed.

Other web sites or other browsers are more secure regarding this issue? Is it possible that one of my add-ons leak? I only have Alexa and HTTP Everywhere. This would be very dangerous.

In 2010 August the following news circulated through the tech media: Private browsing modes leak data

Edit: I just replicated the same error on a freshly installed Google Chrome on a freshly installed Windows 7. The culprit is the HTTPS Everywhere add-on.