For background, see https://github.com/jbosstm/narayana/pull/1403#issuecomment-479495649 and following.
Briefly, in the CDI integration area of ArjunaJTA/cdi, JNDIBean attempts to create an InitialContext. In application server scenarios, the relevant metadata to permit this to happen will exist, and there won't be any issues (so Wildfly etc. are fine here). In CDI SE, it is possible that such metadata won't exist, and a NoInitialContextException will be thrown.
NarayanaTransactionManager uses a similar strategy, but correctly prevents NoInitialContextExceptions from being thrown (https://github.com/jbosstm/narayana/blob/54b60a4db37ca859b9742d5f6f25cc828312ab4c/ArjunaJTA/cdi/classes/com/arjuna/ats/jta/cdi/NarayanaTransactionManager.java#L181).
The proper solution is to ensure that a TransactionSynchronizationRegistry bean is set up in a similar manner to NarayanaTransactionManager.
I'll have a pull request to fix this shortly.