Typically, Android phones and tablets have several volume settings. E.g. my Droid Razr M has 4: Media (including music, video, games), ringtone, notifications, alarms. My Samsung tablet has 3: media, notifications, system. Unless you are in a specific app, e.g. video player, the volume buttons control only one: System on my tablet and Ringer on my phone. Mute function also mutes just that one. So, when my phone muted, a video or a game will play a sound.
I suspect that TTS volume is controled by Media volume.That's Android (or at least device) level functionality.
That's an explanation why it happens this way.
But I agree, that it would be great (and logical) if Aquamail TTS honored system/ringtone Mute setting.