Local Safari history

[hotwater2011]

I'm concerned my son is watching porno and visiting sites he shouldn't. The mac is setup with my iCloud account but iCloud syncing isn't turned on.
Does Safari keep a local file of all the history and websites visited? Even those in Private mode?

 

[hotwater2011]

And there are no extensions like in Chrome (link real time sync, History trends & off the record)?
These can run in Incognito mode but will open any tabs in another chrome browser logged into my account too but creates a local history file on both machines.