Doing some further digging around, the object that is being injected into the DAOs is an instance of org.jboss.jpa.tx.TransactionScopedEntityManager which is located in the jboss-as/common/lib/jboss-jpa-deployers.jar JAR. Looking inside the manifest, the JAR is at version 1.0.0
Looking at the source, it would appear as if the TSEM class should be doing what I thought it should do; that is provide EntityManagers which are only enrolled in the transaction that is currently assigned to the thread.
Still I have no idea why when a transaction is rolled back in one thread all transactions are rolled back. Perhaps this is a transaction management issue rather than an EntityManager problem.