The FAQ reads:
»By default, Delta Chat stores all messages locally on your device. If you e.g. want to save storage space at your mail provider, you can configure Delta Chat to delete old already-received messages on the server automatically. They still remain on your device until you delete them there, too.«
https://delta.chat/en/help#what-happens-if-i-turn-on-delete-...
https://github.com/chatmail/relay/blob/96a1dbac08441034c5990...
https://github.com/chatmail/relay/blob/96a1dbac08441034c5990...
You obviously must trust that the server runs this configuration, but you can always run your own chatmail, or regular postfix. (If you don't need "federation" with other mail servers, you don't even need port 25 open).
However, you can also configure your app to delete messages from the server sooner.