As Symmetra, your goal is to place tiny turrets in deviously brilliant places. Sometimes I'll be placing turrets in areas I'm not directly observing. You're notified when a turret is destroyed, but is there any way for me to get more information about what destroys them? That could be helpful in adjusting my strategy mid-match.
Other than having vision over the area, either directly or through Sonar Arrow, Infra-sight, there is no notification about it whatsoever. They're treated the same as Widowmaker's mines, and both of Junkrat's placeables.
You can't know who destroys them, but you can know when they're fighting because they'll have a small ! over their icon.