Twilio evangelist here.
I think this depends on the specific experience you want to give. For clarity, lets define the two callers as Caller A (the initial caller) and Caller B (the person dialed after Caller A dials in).
Option A
So one option could be to Say the message to Caller A before dialing Caller B. Then when you <Dial>
Caller B, set the url attribute of the <Number>
noun which lets you give Twilio some TwiML to execute to Caller B before Callers A and B are connected.
The downside to this is the parties will hear the message at different times, and you might not want Caller A to hear the message unless they actually get connected to Caller B.
Option B
Another option would be to leverage a <Conference>
. With this option when Caller A dials in you drop them into a Conference instead of Dialing Caller B. Then use the API to make an outbound call to Caller B. When Caller B answers, you drop them into the same Conference as Caller A.
Once Caller B is added to the conference you can have Twilio itself call into that Conference and Say something into it. This SO post shows how to Say something into a Conference:
Use Say verb to all Conference participants
Hope that helps.