I already replied in the ticket but since you also opened a topic here, let me provide the answer here as well
You forgot to mention that you are using Convert forms integration with AcyMailing for that private newsletter list
I think that you should contact Convert form developer because he didn't implement this integration in a way for AcyMailing to send this welcome email
He is not triggering all the functions which would trigger sending Welcome email
You can test this if you publish AcyMailing module which will allow you to subscribe to this private newsletter list. You will see that by doing that, AcyMailing will send welcome email.