I just discovered something interesting. If I hit reply to a toot, it's the time at which I do that that counts as the time I made the toot, and not when the toot actually sends (when I hit the TOOT button).
@WelshPixie that's strange. If that's the case, then the client must be able to set an arbitrary creation time for a message. I've used the API, and it doesn't have that.