Java – Do I want to minimize the scope of @Transactional

Not sure if 'scope' is the correct term here.

I am using Spring for JPA transaction management (with a Hibernate underneath). My method to preform database transaction is private, but since you can only set @Transactional on a class or on a public method

Since this mechanism is based on proxies, only 'external' method calls coming in through the proxy will be intercepted. This means that 'self-invocation', i.e. a method within the target object calling some other method of the target object, won't lead to an actual transaction at runtime even if the invoked method is marked with @Transactional!

I have set the public entry point of the class as @Transactional.

@Transactional
public void run(parameters) {
    //First non-database method, takes a decent amount of time
    Data data = getData();
    //Call to database
    storeData(data);
}

private storeData(data) {
    em.persist(data);
}

Is this bad practice? Is Spring keep an open transaction for longer then needed here? I was thinking of move the storeData() method to a DAO class and making it public, but as academic point, I wanted to know if refactoring to public would have any performance benefit.