Why would you have your phone on while giving a presentation? Also, it's not a very Messenger specific problem - they could do the same thing with your actual phone number.
Well I usually put my phone to silent during class and especially presentations. The person you commented on mentioned there is no silent mode. Of course you could turn the phone off entirely, but then it takes longer to turn on, and you have to unlock the SIM card again... quite a hassle just to make facebook's apps shut up.
I don't know though, I've never used Facebook Messenger.
If you silence your device it will silence everything on it. No noise, no vibrations, no way for apps to bypass it (iPhone at least, and I'm pretty sure it's the same with Android).
