No, they propose just concatenating it with the data received from the network

> it makes a concatenation of the domain separator (@0x92880d38b74de9fb) and the serialization of the object, and then feeds the byte stream into the signing primitive. Similarly, verification of an object verifies this same reconstructed concatenation against the supplied signature.

> Note that the domain separator does not appear in the eventual serialization (which would waste bytes), since both signer and receiver agree on it via this shared protocol specification. Encrypt, HMAC, and hash work the same way

I think not:

> Note that the domain separator does not appear in the eventual serialization (which would waste bytes), since both signer and receiver agree on it via this shared protocol specification.

But saying it's about wasting bytes is a little confusing, as you observe that isn't really the point.

It is definitely not transmitted.

Domain separation happens in the input to the hash function, not on the wire. Because what arrives off the wire is UNTRUSTED input.