Well, I just upgraded to Veeam v9 and guess what? THIS PROBLEM IS STILL NOT FIXED. Why am I not surprised? (for those just coming upon this thread, the short version is that B&R jobs have different notification checkboxes for various types, and UN-checking "notify on success" does not work... you still get an email on success).
It is BEYOND RIDICULOUS that Veeam has been kicking this simple bug down the road for well over a year now, first promising it in a v8 patch, then in the next release. Well, here we are, and it's still broken. Please tell me I'm missing something obvious and it really is fixed, because I'm still getting notified for successful jobs that have "notify on success" UNchecked after upgrading to v9. And Veeam, if you're NOT going to fix this BUG, just remove the option from the UI please instead of making empty promises.