The current tests are sort of trivial because it is hard to see what the class is doing. The member functions change its internal state (maybe), but the accessors are not obviously different after the change.
Maybe we need a dependency injection point to make sure the class is creating new objects for its internal state, or maybe counters that can be used to check that something did happen.
The class is small, and easy to inspect, but this would be a small improvement in testability.