What should I include in the tests for Finite State Machine based framework

I work in the financial industry and the FSM framework I'm referring to is for an Order Management System. It is written using Java, Spring and the rules / transitions are configured in the database.

The current tests are written using JUnit, run using Spring JUnit runner and they cover only the result states at the end of each transition.

For e.g. if an order is Modified / Amended, the integration flow tests only the final outcome i.e if the order status is now Modified in the database or not.

It doesn't test the data that was entered during the modification process actually got persisted in the database or not. There's no negative testing at all either.

My question is, what sort of test cases should a FSM based framework / application have if the framework also has a responsibility of persisting data, publishing data to the down streams, sending reports to customers etc.