[exim] Local and remote names in same domain

In addition to my normal email address, I collect mail for an address at
another domain which for the purpose of this post I'll call
other.mike@???. I have the following router defined for this
domain in the Exim configuration file

my.example.com:
driver = redirect
domains = my.example.com
local_parts = other.mike
data = mike

This works fine and email for other.mike@??? is routed locally to
my mailbox. The problem arises when I receive an email addressed to multiple
users at the other domain, e.g. To: other.mike@???,
fred@???'. When this happens my copy is delivered to me but Exim
then detects fred@??? as a non-local recipient and sends the email
out to my ISP's smarthost with the result that fred gets a duplicate copy.

How do I configure Exim to only send outgoing emails if they originated
locally and to not resend messages which have arrived from outside? I can't
define 'fred' in local_parts because I might sometimes need to send him an
email.

To collect email I use fetchmail to for both accounts and pass the mail over
to Exim, so from Exim's point of view all email has arrived from localhost.

--
Mike Clarke