I don’t think there is a way to “unsubscribe” from assignment notifications. At most, a user can change the Frequency for receiving assigned topics reminders setting, but not the notification when they are first assigned.
I suggest you test it, assigning the user to another topic and checking if they receive the notification. You could even impersonate their account to see it yourself. And all notifications should be in the Notification tab, in their user page.
You could also compare the assignments table and the notifications table, with the Data Explorer. There should be an entry in the notifications table with data like this:
{"message":"discourse_assign.assign_notification","display_username":"constanza","topic_title":"Your topic title"}
The creation date for the notification should match the creation date in the assignment.