There is no thing DeltaChat could do differently (if it doesn’t run in the background and gets the message first to move it there is nothing we could do differently), you need a server-side filter rule or a dedicated email account for deltachat.
Or enable “show emails:all” and use deltachat as only email client, if that is enough for your usecase.
see Sieve rule to move DeltaChat mails to DeltaChat folder
Also some email clients allow you to ignore deltachat messages in their settings (such as k-9mail), so that could be a solution for android at least.
And for thunderbird you can also create filters to move the chat emails on receiving them, but note that those also only run when thunderbird is active.