What I have done for the time being is deactivated Jetpack on the new site.
Looking at your original site, everything is back to normal there.
When you reconnect your new site to WordPress.com, it should indeed create a new data set, and won't conflict with your original site.
I also assume in the future if I want to duplicate sites in this way then I should simply deactivate Jetpack right away on the new site right after the duplication has been completed and then reactivate it in order to prevent those problems from happening again, correct?
Correct. Although I would suggest not copying the Jetpack options at all, if you have access to this kind of settings in the Duplicator plugin.
I did not note down his email address, but is there any way to find out what it was so I can write him a note to apologize for what happened today?
I'm afraid I won't be able to help you there; once someone unsubscribes, we don't keep any tracks of them in our system.
if I do want to eventually activate JetPack on the new site, then I need to setup a new and separate WordPress.com account for the new site so the two sites don't get crossed over again with their stats and email subscribers, correct?
You don't have to. You can connect as many sites as you want to one single WordPress.com account.
The key is not to copy Jetpack options from one site to another, which usually doesn't happen, unless you clone a database, manually or though a plugin.