I'm having the same problems as the OP, but with a different app (Netatmo). No alert tones, but the visual alert on screen works.
I was thinking the problem was with the app, seeing as Netatmo is not a very popular app. But if Facebook app is doing the same, it now has me wondering if it's not the app causing the problem, but ios 9.
I have many other apps what have not been updated for iOS 9, but their alert tones and notifications work just like they did in iOS 8.
OP, your not the only one with alert tone problems.