He feels he doesn't have to explain, and then he's incredibly frustrated when we don't know what he wants
I don't think that's quite what's going on and I don't think he can see it that way - otherwise he'd do something about it. A huge part of autism that NT people are generally clueless about and don't understand is deficits in communication and he's demonstrating a very common one.
He feels he doesn't have to explain
There's a name for this which escapes me at the moment, one of the speech and language tests shows it, it's when someone launches into a narrative assuming you are au fait with all the ins and outs of their situation and then expects you to take action.
That's because they genuinely don't realise that you don't know what they know.
You'll have to get that message across to him and patiently explain that he needs to do a briefing assuming you know absolutely nothing, because his current briefings don't contain the information you need.
Have a read of this article, there's loads about autistic peoples' communication. www.iidc.indiana.edu/pages/Social-Communication-and-Language-Characteristics-Associated-with-High-Functioning-Verbal-Children-and-Adults-with-ASD
This bullet point is close Have difficulty knowing that he or she has the responsibility to give the communication partner sufficient information to understand the message. In addition, he or she may have difficulty surmising what information the partner already has and what new information is needed
Frustrating as it is for you, it's not his fault, he's autistic and that's how he's wired. He doesn't instinctively know that he's not giving the right information in his briefings, he cannot intuit that from your responses unless you patiently explain to him exactly what information you need from him.
He thinks he's given you everything you need to do the task, you need to let him know what else you need in order to get the result he wants.