It's not leaving the grass that's the problem, it's moving far enough away that the shaking patches are off-screen. Say you pick a shaking patch on one side of the Garden, and the other 3 patches are generated in non-grass spots off to the side. If you walk to the other side of the Garden, that would definitely put those patches off-screen.
Trophy Garden's kind of a hard spot to chain in because of the missing patches. You can still get an early shiny patch if you luck out. I got a Nincada in Eterna Forest that way a few days ago.