I’ve gone through the settings and should only be getting notifications that directly apply to me (account stuff, direct replies, follows, etc), but the notification function on the site is a hot mess. It’s like the cross-walk button on a street corner, a “nuttin’ button” — you can press it until the cows come home and it ain’t doing nothing!
Maybe you will have better luck. Click on your user name (upper right corner) and click “Account” in the pop-up. You should see “Notification Settings” after that. Good Luck!!