PostFix null client and multiple domains (virtual hosting)?

[FractalizeR]

Hello.

I'm running PostFix on my server in null-client configuration. So postfix is used to send email only. I receive email via external email provider (Yandex mail for domains). I set my domains MX records to point to provider ones.

The problem is that my machine has several domains running on it (with php in fast-cgi configuration). And when PostFix sends email in SMTP session it says something like:

C: HELO hostname.com
S: 250 Hello hostname.com, I am glad to meet you
C: MAIL FROM:<username@hostname.com>

Where username is the name of the system user, that invoked sendmail, and hostname is the hostname of the server.

Body of email message contains a valid email address in headers.

The problem is that many email servers reject emails on MAIL FROM command with invalid email address specified.

How do I correctly set PostFix mapping so that each Linux user had a corresponding email address to be used in SMTP communication?

I've tried to setup mapping in the /etc/aliases file and putting them to alias_map directive of main.cf, but somehow it doesn't work.