I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
You are in no way responsible for delays caused by the airline. The customer has no legal basis for calling you and yelling at you, just because he's upset with what happened. The airline is the one who would owe him (if he's entitled to compensation at all). You do not have any obligation to give him a penny back, and if he sues, a judge will not order you to pay him.
You also have no obligation whatsoever to talk to him. You can let him know that all further communications must be via letter (or just tell him not to contact you again, period), and block his number. If he calls, tell him you will not speak to him until he can be reasonable and hang up. You do not have to return his calls. You can send him to voice mail and ignore those messages (keep them, in case you need evidence, though). But you didn't do anything wrong here.
The law does allow someone to contact another person if they believe they're owed money, so it's not illegal for him to call you. But once you tell him to STOP, if it continues, he could be charged with harassment. Threatening physical violence is also illegal, and you could contact the police if you believe he's going to follow through.
If you have any questions or concerns about my response, please reply WITHOUT RATING. It's important that you are 100% satisfied with my courtesy and professionalism. Otherwise, please rate my service positively so I am paid for the time I spend answering questions. If you are on a mobile device, you may need to scroll to the right. There is no charge for follow-up questions. Thank you.