I did not investigate this in a lot of detail, but it looks like the flyout navigation is caching category title a bit too much.
When visting publicaiton A, and then visiting publication B, the flyout navigation will show sub-categories of publication A. The URLs though are correct, it is only the sub-category title which is from publication A.
I looked at the requests going to the e-commerce service. It looks the category request and responses are correct so I suspect this is something on the webapp side, in the E-Commerce framework.