Lets look on the definition of Private Browsing here:
https://support.apple.com/kb/PH19216?locale=en_US
When you use Private Browsing windows, Safari doesn’t save your browsing history, and it asks websites you visit not to track you.
and here:http://en.wikipedia.org/wiki/Privacy_mode
Privacy mode or "private browsing" or "incognito mode"[1] is a privacy feature in some web browsers to disable browsing history and the web cache. This allows a person to browse the Web without storing local data that could be retrieved at a later date. Privacy mode will also disable the storage of data in cookies and Flash cookies. This privacy protection is only on the local computing device as it is still possible to identify frequented websites by associating the IP address at the web server.
So this means that Selenium is equivalent to turning on Private Browsing. Every time you start any driver via Selenium it creates a brand new anonymous profile, you are actually browsing privately. (if you do not use already created profile of safari)
BUT! If you still think that you need to run safari in incognito mode, you can use the following hack:
you can automate the process of enabling the Private Browsing option with AppleScript. Like so.
First, launch the Universal Access system preference and enable the Enable Access for Assistive Devices option.
Launch Script Editor (within the AppleScript folder inside the Applications folder) and enter the following script:
tell application "Safari"
activate
end tell
tell application "System Events"
tell process "Safari"
tell menu bar 1
tell menu bar item "Safari"
tell menu "Safari"
click menu item "Private Browsing"
end tell
end tell
end tell
end tell
end tell
Info from here: http://www.macworld.com/article/1139714/enableprivatebrowsing.html