I know it's an Exim error message.
That is odd, because whitelists should overrule that anyway. Did you tried multiple whitelists and also restart Exim after making the additions?
But it's a bit confusing anyway.
I don’t want to send from that domain. I want to receive mail to that domain.
To be able to receive something, something else needs to be sending things even if it's to localhost. So your old server is sending, that is what I mean.
Now what exactly is it about. Is it a hostname or is it a domain?
Because if it's a domain, then a better example would be user@oldserverdomain and user@newserverdomain otherwise I think it's a hostname.
Also I don't know if (in case of a hostname) it's smart in this case, to point to A record to the new server's ip, maybe it's better to use another solution.
But I'm just fishing, way too little info to be able to give a good advise further.
Maybe fastes is to quickly start changing the mails in the monitoring tools.