I used to get double notifications, but that was before I changed some settings and got rid of some check marks on the “settings” page.
“Someone posts in a discussion I’m following” is the only notification I really need to stay on top of threads.
Turning on the setting: “Notify about every new post instead of only the last in a discussion” will cause a lot of notifications.
I also got rid of the checkmark for: “Someone replies to one of my posts”
Long story short: look at the settings page.