Yes the postPersistAnimal method will be invoked. All the callbacks defined by the superclass entities or mapped superclasses will be executed when updating the subclass entity. This behaviour is specified in the JPA documentation.

If a lifecycle callback method for the same lifecycle event is also specified on the entity class and/or one or more of its entity or mapped superclasses, the callback methods on the entity class and/or superclasses are invoked after the other lifecycle callback methods, most general superclass first. A class is permitted to override an inherited callback method of the same callback type, and in this case, the overridden method is not invoked.

You can find more info regarding the execution order and other details here.