The way packages are validated actually is through the same channel as you download the packages themselves from (IE your mirror), they just are signed with the Debian package signing key(ring), of which only a select few maintainers have authorized private keys for.

This does mean an adversary (whether a MITM if you're using HTTP or malicious operator on the mirror server itself) can technically serve you old versions of an (officially signed) package indefinitely and your package manager would be none the wiser, but otherwise this approach actually works quite well.