How to unit-test in “tell, don't ask” follower classes?

Question

I think the issue is explained best with an example.

public class MyService {
    private OtherService theOther;
    public void setTheOther(OtherService srv) { theOther = srv; }

    public void myBusinessStuffFor(int id) {
        theOther.applyToAllWith(id, new OtherService.Action() {
            public void apply(Object whatever) {
                doTheHardBusinessStuffWith(whatever);
            }
        }
    }

    private void doTheHardBusinessStuffWith(Object whatever) {
        // here the business stuff provided by MyService
    }
}

public interface OtherService {
    void applyToAllWith(int id, Action action);

    public interface Action {
        void applyOn(Object whatever);
    }
}

I like this pattern, because it's very cohesive. Action interfaces are paired with their Services. Business logic is not cluttered in many classes. Subclasses are only providing data to the action and don't have to be busy. I adopted it from here ( http://jamesladdcode.com/?p=12). The problem is that i didn't found a good solution for testing the behavior in the "doTheHardBusinessStuffWith(Object whatever)" method if i mock the otherService. With the mock i have to care how the business method gets called. But how can i do this. I use mockito and tried it with a ArgumentCapture already. But it don't feels right because of abusing ArgumentCapture.

I would like to know if the pattern used in class MyService.myBusinessStuffFor(int id) has a name (is it strategy pattern)? But my major questions is how to make this code testable with mock of OtherService?