Oh, my. You are doing it right. I don't understand the way the teacher is thinking. We do what works, not what some book or rule says.
I've had lots of experience with this sort of behavior both from children and adults. I'm a retired police officer and there are some officers who act the way the teacher wants to act. They get in people's faces and start a fight. It just does not work. I was a part of a group of officers who trained with a psychiatrist and a psychologist to learn how to deal better with individuals. We learned to give people who respond by just standing with their arms crossed space in which to process the information. If they move, are agitated or in any way are responding in a negative way then we must stop their activity. That does mean looking them in the eyes and often physically restraining them.
Your son is responding this way because his mind is thinking about what has happened and how to respond. This is a reasonable way to respond. Because he's not continuing to act out or openly defying the adult he does not need to immediately be put in time out. The time out happens when he doesn't comply. The goal, after all, is to gain compliance. Until he takes some sort of action he is complying.
I suggest that the school can use the same technique. I suggest that you talk again with the teacher, explaining why this works at home and why she doesn't have to take immediate action. Yes, she doesn't have time to wait until he's ready to talk but she can schedule in time to talk. She can wait the part of the part of a minute it takes him to decide on how he's going to react.
My grandson is autistic and in special ed. The way you describe responding to your son is the way the staff responds to their students. I don't understand why the staff continues to do what isn't working. Perhaps you need to talk with the school counselor who is likely to understand better what you're trying to say. The counselor could then be an intermediary with you and the teacher.
I would stop taking toys away when he gets a bad report. It's too long after the event for him to connect the toy with the behavior. He's apt to be angry at losing the toy and does not understand why he's lost it.
It's good to have rewards for good behavior. When he's been well behaved all day the reward is soon after the good day. But the discipline of removing the toy is not closely related to whatever behavior earned him a bad report.
I suggest that you don't need to do anything when he gets a bad report other than to talk with him about why and how he can do better the next day. The goal of discipline is to teach. Focus on the teaching.
I'm a big fan of Love and Logic by Foster Cline and...... You may get some reinforcement for your way of handling your son that you can show the school staff. Also ways to reinforce good behavior and give the responsibility for poor behavior to the child. Natural consequences is more effective than punishment. Taking away his favorite toy is punishment, unconnected to his behavior.
Giving him treasure when his day has been good may not be the best thing to do either. I suggest praising him would work just as well and would teach him that good behavior has it's own reward. You want him to behave because it's the right thing to do, not just to get a reward.
After reading the previous post, it might be a good idea to spend some time in the classroom to see how they do handle it and then modify your response to something similar. You can teach him to not hit or be aggressive by immediately giving him a time out to calm down. Tell him that hitting is never OK; that you won't let him hurt you while you grab his hands.
I suggest that time outs for aggression need to be less structured than other time outs. He needs a way to get rid of the energy that his anger has given him. I send my grandson to a quiet spot to recoup. We talk about how he needs to calm down and so should stay in his room until he's calm and can come out and talk about what happened. That way he can move around and get energy out.