CA - If you're under the limbs with a tiller, aren't you tearing up your roots? I always thought most trees have a root system about the same diameter as the tree itself.
I think our farming here is unusual. No rain from Easter to Thanksgiving, to oversimplify a little. Everything has to be deep rooted to survive. My neighbor who commercially operates/harvests this orchard for me says he has found what works best is he discs once a year in early May when the grasses dry out and turn brown, to turn under the native grasses and cover nitrogen crop he planted last fall.
He says discing breaks up the capillary action pulling moisture up out of the soil into the cover, and disrupts the gophers a little. My rototilling is to turn over the small areas that his big 8 ft disc can't reach - corners etc.
Both the disc and the rototiller climb, jump, over any larger roots they encounter. I think the surface roots you are thinking of have already dried up by the time the ground cover has browned.
Here's a photo where I rototilled before placing a new tree. As the ground dried out, no grass grew in the tilled area. The background shows the late-spring browning/drying out that I described.
Most of California uses irrigation for farming. This dry-farmed orchard is a relic of practices here 120 years ago. My neighbors have all ripped out their apples and have drip-irrigated vineyards now.