After you have activated Domain Privacy, it may take a while before your information is updated in the various WHOIS look-up websites.
A website stores content locally and only periodically checks if data has changed. If you still see your personal information listed, this means that the website hasn't looked for updates yet.
One.com has no control over when a website updates its content, but normally it should not take more than 24 hours.
Tip: Make sure to also clear the cache that is stored in your own browser.