Postfix - relay issue on my end?

Question

Maybe someone experienced more than me in Postfix can help me out a bit.

mail.log:Dec 11 22:14:36 server596 postfix/smtp[31301]: 3A5BC17AC00D: to=<[e-mail]>, relay=njsbw.com[1.82.230.122]:25, delay=236296, delays=236295/0.01/1.1/0, dsn=4.4.2, status=deferred (lost connection with njsbw.com[1.82.230.122] while receiving the initial server greeting)
mail.log:Dec 11 23:24:37 server596 postfix/smtp[20292]: 3A5BC17AC00D: to=<[e-mail]>, relay=njsbw.com[1.82.230.122]:25, delay=240497, delays=240495/0.01/1.8/0.44, dsn=5.0.0, status=bounced (host njsbw.com[1.82.230.122] said: 550 Local user only or Authentication mechanism (in reply to RCPT TO command))

These are two example lines from the log.

The actual issue is that one of my mail users receives hundreds of emails per day, they all are messages from my mailserver informing him that a mail he sent went bad.
The line is an example of a recent "failure".
He did not send those emails and his PC seems to be clean from possible trojans.

What I tried:
I logged in my server from a foreign IP to port 25 and tried to relay an email.
I got the proper response 554 5.7.1 <[e-mail]>: Relay access denied

So it seems like relay access is properly working but I am not entirely sure what action can cause the above log lines.
As relay access seems to work (requires to log in), what else can cause that ?

Here the message text of one of the problem emails:

This is the mail system at host mail.myserver.com.

I'm sorry to have to inform you that your message could not
be delivered to one or more recipients. It's attached below.

For further assistance, please send mail to postmaster.

If you do so, please include this problem report. You can
delete your own text from the attached returned message.

                   The mail system

<[e-mail]>: host njsbw.com[1.82.230.122] said: 550 Local user only or
    Authentication mechanism (in reply to RCPT TO command)

P.S.

smtpd_recipient_restrictions =permit_mynetworks, permit_sasl_authenticated, reject_unauth_destination