Particles that are a part of a transverse wave oscillate perpendicular to the propagation of the wave. So, if the wave moves along the x-axis, then the particles must move in the yz plane and mustn't move in any direction parallel to the x-axis.
The particles themselves are in the xy plane, but look at the arrows. The velocity of any given particle is 100% perpendicular to the x-axis. The particles may move in the y direction; they may move in the z direction. Heck, they may even have velocity components in the y direction and in the z direction. It doesn't matter. Knowing the fact that the transverse wave propagates along the x-axis, it is safe to say that the particles are oscillating in any arbitrary orientation in the yz plane. We cannot say that they are doing the same in the xy plane or in the xz plane.