It sounds like you've got the social connectors (data set and data flow) set up and the system agents (AutoCreate Cases and Process Threaded Documents) running, since you're able to harvest relevant tweets and bring them into the Pega Customer Service interaction portal. That's great.
For replies, you need to do the following...
Configure the Response Authorizations, which are accessed from either Designer Studio (Channel Services > Pega Social) or Pega Express (Settings > Social) , depending on your Pega Customer Service version (what release are you using?). For the 7.4 release, see page 102 of the Customer Service 7.4 Implementation Guide.
Authorize each operator who will be responding to social posts to respond (this is done from the operator's Preferences area). For the 7.4 release, see the bottom of page 97 of the 7.4 Implementation Guide.
If you're using Pega Customer Service 7.31, you can get to the Customer Service 7.31 Implementation Guide from the documentation archive page.