The most appropriate way to do that is outside of SAS RTDM. For real-time triggered outbound campaigns with SAS RTDM, normally you'd have some sort of middleware or an integration adapter that processes events and makes a request to SAS RTDM campaign.
You will need to implement an integration capability into that middleware or adapter. Make it interpret SAS RTDM's response ("Email" and "SMS" response channels) and act accordingly to that response - actually trigger channel APIs to send these messages.
That is a simplified vision of architecture that we normally build for our clients, and done it successfully on many projects (we even have a reusable Java framework we use to building these "integration adapters").
If you are using SAS ESP for initial events processing and trigger SAS RTDM (not everyone does), then it is possible to leverage an out-of-the-box REST subscriber adapter to have ESP making a call to RTDM, and then having RTDM response sent back to ESP (into another source window) - so that SAS ESP could then process the response, and initiate the actual SMS or Email communication using its adapters. This allows minimizing custom coding (you may not need that customized "integration adapter" component in this case) but it comes with a separate set of complexities and limitations. Some of our clients decided to implement a customized integration adapter even though they used SAS ESP for initial event processing. There are tradeoffs and choices to be made.
Another option you can hear about is to use the Process Node (written in DS2 or Groovy language) to initiate an outbound API call from within the RTDM diagram (before the Reply node). Which I don't recommend. Before the processing has reached a Reply node on a diagram, you don't have Treatments assigned, don't yet have important identifiers (response tracking code, treatment tracking code) required to track this contact and correlate it with the Contact and Response history in CDM, etc. It can be used to send an email or SMS as a quick prototype, but we do not recommend this as part of an integrated production solution.
The proper way is to rely on Reply nodes and then having something outside of RTDM (the "integration adapter", or SAS ESP) processing the response and acting accordingly (actually sending the communication, etc.).
Hope this helps!
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Dmitriy Alergant, Tier One Analytics