I've been running Mate and Gnome3 for the past 6 months as well. Mate had some issues and, for both, the screen went black for 1-2 seconds when videos start playing.
I was able to get a compositor (Compiz) working on Mate and this fixed the tearing issue. It had some issues where it just kept crashing and rebooting that I never figured out. So I switched back to Gnome3. Although Gnome3 comes with a compositor (I think? And I think it might be Compiz?), I can't seem to get rid of the screen going black when a video starts.
But it really doesn't make a big difference and it's not a big enough annoyance to matter. I don't really use FreeBSD for media anyway. It's just the auto-play videos on Facebook that triggers the infrequent frustration.