In SSL 3.0 and TLS versions 1.0 through 1.2 the last two messages are the "Client Finished" followed by "Server Finished" messages. These messages include an encrypted (under the established session keys) MAC of all the previous messages.
However, in TLS 1.3 and in the abbreviated handshake, the server is the first to send a "Finished" message, not the client.
I'm trying to understand if the order has some significance in regards to security, but I believe the answer is no. Replay attacks are not possible because of the nonce values, and MITM attacks (that would be impossible because pre_master_secret is encrypted under the server's public key and used by the client to establish keys) would rely on the attacker establishing keys with both client and server, which wouldn't matter when it comes to who sends the finished message first.
My question is, does it matter from a security point of view whether the client or the server are the first to send the message? What's the rationale behind the changing order?