Please note that chat and email contacts are the only one that are forwarded from SM to UCCX. Other social contacts such as Facebook feeds, Twitter feeds etc should only be handled using SM since there is no mechanism to forward them over to UCCX and then let UCCX find an available agent as it does for chat and email contacts.
However there is a way using which you can allow the SM campaign page (which includes Twitter feeds, Facebook feeds etc) to be opened directly inside Finesse desktop and let the agents handle them that way then. For this, you will need to add below lines to the XML layout that is being used for Finesse desktop
<tab>
<id>SocialMiner</id>
<label>SocialMiner Campaigns</label>
<gadgets>
<gadget>http://<FQDN of SM Server>/gadgets/campaignResults.jsp</gadget>
</gadgets>
</tab>
After doing above, ask the agent to log out and then log back in Finesse and they will be able to see a new tab SocialMiner Campaigns as shown in screenshot 1 attached to this thread. In order to allow the agents to login into this SM gadget, you will also need to integrate SM with AD since their credentials will be directly authenticated against that and not the one that they will be using to login inside Finesse desktop. Refer to below guide in order to configure AD with SM:
http://www.cisco.com/c/en/us/td/docs/voice_ip_comm/cust_contact/contact_center/socialminer/socialminer_1101/user_guide/CUSM_BK_CC689091_00_cisco-socialminer-user-guide-1101.pdf
Once the login is successful, then the agents will be able to see something like Screenshot 2 and they can then reply to the feeds.
Regards
Deepak