Hi, Igor. I'm not sure which version of the presentation you've seen. Look through http://blog.thecodewhispere... and perhaps that'll help you with more details, but in short, to keep server and client code tests in agreement requires discipline. As of early 2016, nobody has produced a tool to automate this, and I don't think such a tool is possible.
I use a simple system: I know the correspondence and I look for it. It's exactly the same to me as checking that comments and code match, then fixing them when they don't, often by removing the comment. :) A stub in the tests for the layer above corresponds to assertEquals() in a test for the layer below and an expectation in the tests for the layer above corresponds to an action in a test for the layer below. That's it.
Especially if different teams write the server and client, then you simply have to talk to each other. You can't get around it. As the client, I'd use the contract tests as a classical acceptance test suite for the server: if you don't pass these tests, then I can't use you. When the tests fail, we have to negotiate which side changes their behavior. :)
A gap is inevitable only in the sense that we're imperfect beings.
I hope this helps.