[exim] qualify_domain ignored

Hello,

I've two hosts with an Exim installation. I want to get locally created
mails send to my admin mailbox.

That works if I create a mail via the pattern
$ mail admin@domain

But it doesn't work for
$ mail admin

I thought Exim would qualify the domain part for me when setting the
qualify_domain – but it doesn’t (also tested with qualify_recipient).
Instead the from and to is expanded with @hostname.domain, therefore the
mail recipient isn't seen as local and the delivery fails.

Why is that?

Regards,
Christian