I'm pretty sure I finally know what causes all the low times in Team Two.
If you are attacked and fall off the stage, and restart on the very last frame before you would die, you are able to move around and attack the other team before the four-second animation takes place. The issue here, obviously, is that a similar technique in Sonic Adventure 2 (used for 8"25 mission 2s) is already banned.
Now I can't say that this is what happens in the low times with absolute certainty because it's been such a long time since I got 5"34, and even so, why are there ten such times on T2-Rose, and none on any other team battle?
Let me know the results of any testing you might do to resolve this one.