Mastodon: Your DMs can be read by the admin(s) on your specific instance.
Twitter: Your DMs can be read by the entire Twitter Corporation.
@tinker *Mastodon: and the admin of the possibly-remote instance you're sending the DM too, which would more likely be the issue.
This is a private instance. Sorry.
Go check this list of instances or this website to find one suitable to your needs. :)