Gail Badner to trigger the association management, at some point there has to be a change in the *ToMany field, even if it's with the same collection. The collection itself is not tracked for changes.

So, instead of:

customer.getInventories().add( customerInventory );

It's required a call to the setter:

Collection<CustumerInventory> inventories = customer.getInventories();
inventories.add( customerInventory ); 
custumer.setInventories( inventories );