In theory, when you add a new trigger or action for "Office 365 Outlook", you have choice of creating a new or using an existing connection. By default, it will use any existing connection it finds. The bottom of the tile for the step will say "Connected to ..." followed by a "Change Connection" link. That link should allow you to create and use a connection to a different mailbox.
When creating a new connection, Active Directory may try to be helpful and sign you in automatically to the mailbox of the current user. If you don't get a chance to log-in as the secondary mail account, you may have to copy the URL that appears briefly right after the loading page (the one that starts with login.microsoftonline.com) and open it in an InPrivate window (for Internet Explorer) or Incognito window (for Chrome).
