The Atari could certainly do that split-screen stuff via the "Display List". The Amiga was partially based off of the Atari. Some of the same engineers worked on the Amiga. It even has a more advanced version of the Atari's Display List functionality.
And screen tearing stopped being a problem with the Atari. But usually only games try to v-synch with the screen. Those, and some text file viewers which support smooth scrolling. Of course you won't see anything like that in a window system; only full-screen programs. And remember that if you try out one of these old machines in an emulator, that your monitor's refresh rate must match, or be a multiple of, the emulated computer's refresh rate to see smooth scrolling.
(make sure to activate the emulator's "vsync" feature as well)