You can use the follwing sample connection file for replication:
<?xml version="1.0" encoding="utf-8" ?>
<connection xmlns="http://www.layer2.de/schemas/cloudConnections" interval="60" version="1.2" enabled="true">
<dataEntities>
<dataEntity name="Twitter"
type="source"
provider="System.Data.RSSBus.Twitter"
connectionString="User=myUsername;Password=myPassword;Auto Cache=False"
primaryKey="ID"
selectStatement="Select * from FriendsTimeline">
</dataEntity>
<dataEntity name="SharePointDestination"
type="destination"
provider="Layer2.SharePoint.Provider"
connectionString="Data Source=https://mydomain.sharepoint.com/sites/mySite/;
Initial Catalog=Twitter;
Authentication=Office365;
User Id=myUser@myDomain.onmicrosoft.com;
Password=myPassword;"
selectStatement="">
</dataEntity>
</dataEntities>
<fieldMappings autoMapping="true" >
<fieldMapping>
<field entity="Twitter" name="Text"/>
<field entity="SharePointDestination" name="Title" />
</fieldMapping>
</fieldMappings>
</connection>
The RSSBus Twitter Driver for ADO.NET is used as data source provider. You can use several views to access certain feeds, search for keywords, connect the followers list or the list of persons you are follow. See documentation for this. This example uses an Office 365 list as data destination. Updates are every hour in this case, but can be done more frequently if required.

Fig.: Twitter feed in a native SharePoint list.
Please note: After synchronization with Cloud Connector you have the content in a native SharePoint list, on-premise or in the cloud. That means, you have full integration with search, lookups, workflow, RSS, email notification etc. You can place list web parts wherever you want.
In the same way you can replicate almost any data sources to almost any destinations using the Cloud Connector. Here is a sample configuration file entry, that replicates Twitter to a SQL Server table TwitterFeed:
<dataEntity name="SQL"
type="destination"
provider="System.Data.SqlClient"
connectionString="Data Source=srvsql01; Initial Catalog=Northwind; User Id=MyUserID; Password=MyPassword"
selectStatement="Select * from TwitterFeed">
</dataEntity>
Please read more about the Cloud Connector here.