If any email address is listed only for a person, then any emails from that email address will only appear in the timeline for that person if auto-shared.

Therefore, for an email to show up in a organization timeline, the email has to be added to a work item for the organization or manually added to the organization timeline.

If you wish to have all emails from that email address to be auto-shared on the Organization timeline, you can add the email address to the Organization's details tab.