Who is supposed to reach out first after an intro email is sent? The client or the hero?

The flow for matches in the system is that, once a match is established, an introduction email is sent out between the client and the hero. At that point, either the client or the hero can send the first message - generally whoever gets to it first. 

One point of confusion that we have run into in the past is that the client may think that the ball is in the hero's court to reply first, or the hero may think the same.

The ball isn't necessarily in one person's court at this time. The reasoning behind this is that the Commerce Hero platform, to a large extent, is built off the idea of trying to scale the types of high quality introductions that are made organically between professionals.

If you think about an organic introduction email that was sent between you and someone else, there isn't a clear call to action as to which of the two parties is supposed to reply first. It's an introduction between professionals and usually both parties will care enough about the introduction to take a moment to reply.