We use Jitterbit Studio and currently we do batch data movement from salesforce to Epicor and other way also. These data syncs are scheduled overnight, for this purpose native jitterbit salesforce connector and rest api's on Epicor side are leveraged.
For a new business requirement, we are looking to see if real-time data sync mechanism can be established. Within salesforce i am aware it has a outbound message mechanism where it can call an external web endpoint and pass data as xml (soap).
For other systems that might have a publish/ subscribe kind of system where jitterbit is a subscriber, does jitterbit have any feature that allows it to become an event subscriber for an external system publisher.
We use Jitterbit Studio to craft our integrations which is a non-cloud version within their suite of integration solutions and within this landscape i have researched within the jitterbit community with no answers hence coming here to stackoverflow as a last resort.
Jitterbit absolutely supports real-time data flow. The most common ways to handle this are through APIs and SOAP web services. Jitterbit can receive an API call (e.g., a webhook notification) or a SOAP call and run an operation using the data received. There are potentially other options, depending on exactly what you need, such as having the "message" saved as a file in a folder and having Jitterbit check that folder for new files as often as every minute (not truly real-time, but close enough).