So does a JIS screwdriver work in Phillips screws (not cam out like Phillips drivers tend to do)?
Phillips screws and drivers were designed so that it limited the torque applied to keep ham handed assembly workers from stripping threads on the screws.
From the info presented, JIS screws and drivers eliminate the cam-out issue, but it's not clear that a JIS driver will work any better than a Phillips driver in a Phillips screw.
Robertson (square drive), Allen (hex recess), and torx (modified hex) serve the same function (eliminate cam-out) but of course you can't use those on Phillips screws.