The concept of JMS is based on the sharing that is a major difference with the duplication of content that require to synchronize the data.
If your description, it seems that you didn't share the K2 content but have 2 websites (a) and (b) that have their own K2.
So this is normal that you don't have the same content as you didn't share it.
See the tutorial video 16 on how to share the content of an extension.
This is illustrated for the users but also applicable for the extension that can be shared.
See the list of extension that can be shared.
www.jms2win.com/en/list-of-extensions?vi...id=269&Itemid=53