I *think* the reasoning here is as follows:
The voice you hear is just ADA reading your emails to you - that is why the messages are called emails, why they have an email icon, and why the message box shows ADA@ficsit.biz; so, when Steve sends you an email, ADA still just reads it out for you.
This isn't obvious, and ADA doesn't mention that this is what is happening, but it makes sense. Perhaps adding "New email message from: Steve" to the start of the voice sample would make this less bizarre and confusing - as it stands now, she just keeps talking while the address changes from ADA to Steve, with no notice that the messages are even separate in any way.