Not a tips, just a 'guess' after a little observation. Maybe someone can confirm this.
So some plants' attack hits even those zombies outside the lawn, or before they step into the lawn. We know that there is a certain distance outside the lawn where zombies start to appear and slowly walk into the lawn.
The attack may not be triggered before the zombies enter the lawn, but in the case of Plant Food-fed attack or prolonged attack (projectile) which goes further out of the lawn and hit zombies outside the lawn (since the zombies who triggered the attack has been killed early and let the projectile hit the next zombies which haven't been on the lawn).
Now the thing is, when I use Tumbleweed, especially when combined with Blover, I feel like the zombies appear less, despite that I easily take care of the waves. Well, my Tumbleweed has grown to its adultest phase, for the record.
This is more apparent when I use Tumbleweed + blover in Arena level. Even when I Tumble-Blow zombies quickly enough and take care of most of the waves before they enter mid-lawn, the score is pretty low. And I noticed the zombies seem to appear less.
TLDR: So my verdict is that the Tumbleweed keeps bouncing and attacks some zombies even beyond the lawn. So when they toss or knock-back (with Blover's blow) the zombies outside the lawn, they already killed them there. Therefore, fewer zombies appearing and entering the lawn (fewer score in Arena).
Again it's just a guess.