The membership of a group is composed of distinguishedNames, not e-mail addresses. If you want timanov@keyman .com (a user) to use a different e-mail address then change that user's primary SMTP address. The same would be true for ALL the members of the DL if you want them to use a different SMTP address when sending an e-mail.
In other words, the distribution group doesn't care what a member's e-mail address is because that information will be retrieved from the object whose distinguishedName is found in the members property of the DL.