When you create a new contact, your emails with this person will have the Auto-share setting turned on. With this setting turned on, any emails between you and a saved contact will appear on their timeline. If you do not wish to share your emails with specific contacts, be sure to turn off Auto-sharing by clicking "Turn Off Sharing" in the grey box after the Email Address field.
Your communication will remain private unless you choose to change this by clicking on the link highlighted in blue on the right side and toggling the sharing to on.
There are a few other rules to consider about private emails:
If you create a new contact from an email in triage, the contact will automatically become public unless you click "Turn Off Sharing".
If you assign an email from a private contact to yourself, the email will appear in your to-do list, but colleagues who are not members of the client team for that contact will not be able to see it.
If a public contact is cc'd on an email from a private contact, that email will be visible on the public contact’s timeline.
If you create a contact using the global "+" button or from the Contacts area, your email communications will automatically be shared on related timelines unless you click "Turn Off Sharing".
If you would like to remove a specific email from a timeline (for example, you are having a non-work related conversation with a client), you can remove it by clicking the "x" on the briefcase tab of the information tray.