The sentence highlighted means that clients that support asynchronous subscribers process messages in callbacks, asynchronously, and clients that have sync subscribers process them in place (or pass them to another goroutine/thread/etc).
NATS queue subscriptions (in both NATS core and NATS streaming) will fan messages out randomly between queue subscribers, not waiting for a response. If you have ten messages sent to two queue subscribers (A and B), queue subscriber A might process messages 1,3,4,6,9 and queue subscriber B would process messages 2,5,7,8,10. These may process messages at different rates, so with queue consumers NATS does not guarantee delivery order.
If you need to serially process messages between multiple queue subscribers, you'll need some sort of coordination - this may be a distributed transaction coordinator or a distributed lock.