It sounds like transitional issues to me. And not for nothing, but if he's in a special preschool designed for special needs children including those on the Autism Spectrum then they ought to know you can't rush a child like this. "Quick cooperation" is not in our vocabulary.
Have them set up a schedule board for him. I suspect he's in the process of learning to read so they can do this with a series of clocks and images of the activities that will occur that day. They can also include the words used to describe the activity. Prior to the change in events and when they need him to perform certain tasks they will need to give him warnings that it's going to occur.
9:00 Sign In and Put Coats Away
9:05 Wash hands
9:10 - 9:50 Circle time
9:50 - 10:00 Bathroom break
10:00 - 10:30 Free play
10:30 - 11:10 Arts and Crafts
11:10-11:20 Clean-up
11:20-11:30 Bathroom break
11:30- 12:15 Recess
12:15-12:25 Bathroom break and Wash hands
12:25-1:00 Lunch
and so on and so forth
It's not "quick and easy" but it will be time efficient when push comes to shove. This will also serve a few purposes... help him learn to read by associating images with the words and help him learn to tell time. He'll also become invested in the schedule and the routine. If he likes routines as many other kids with Autism do, then this will be right up his alley and he'll enjoy knowing what to expect next and when to expect it. It will give him a sense of control and stability as well as continuity. He won't be surprised.
And this will be a great tool for the teachers because if there's a short day of school they can create a separate schedule board for days like that and if there's a day where the schedule is going to be different then they can adjust it by superimposing the appropriate images and words over the existing scheduled activities if they attach everything with velcro and laminate everything.