E-Mails keep bouncing due to bad header - How does phpList even work?

I installed phpList a short while ago and on the technical side it works fine. But whenever I send a test campaign, the E-Mails bounce or are moved to spam. This is because phpList keeps throwing the E-Mail of one of my phpList admins in, which is not registered on the sending server.
I have consecutively tried the following things, since none of them worked: changing the E-Mail of the original admin user to one that is registered on my server
deleting the original admin user and creating it from scratch with the right E-Mail
deleting the original test list and recreating it with the proper user
The bounce message always tells me that email2@domain2 is not allowed from this IP address. I changed to email1@domain1 everywhere, but in the mail source code email2 still shows as list owner and return path
sending E-Mail directly works fine to all addresses.

You will need to be clearer as what you mean by this.

When you set up phpList through the web interface, you are asked to create an admin user with an email address. I used email2@domain2 as that address, because it’s the one I use for web administration. It is not the one I use for sending phpList emails, those go through my own smtp server on domain1 using email1. So when I actually receive an email I sent, the from-part in the mail program says email1@domain1, since that’s what I now enter in the draft field. In the header, however, you will find email2@domain2 in numerous places, which causes the email to bounce, because my smtp host is not allowed to use this email, since it belongs to domain2, not domain1

@some_it_guy The admin email address should be on the same domain as phplist because it is used as the From address for “system” emails.

I’m not sure which headers you are referring to that contain the admin email address. Possibly the envelope-from address if you have not set the $message_envelope variable in config.php.

I had already setup a new admin with the right address and deleted the old admin
For some reason the address still showed in envelope-from and list-owner, even though i had deleted the list and recreated it with the new user.
Setting the message_envelope finally fixed the bouncing, even though i am not sure that it should, because the original email should not have been stored anymore anyways, but thank you.