From my point of view from the moving travellator, the ball was moving vertically up and down.

But from the point of view of a stationary observer, the ball was moving in a parabolic path.

This video illustrates the fact that projectile motion is basically a vertical throw superposed with a horizontal constant speed motion. The vertical and horizontal motion are mutually independent and can be analysed separately.

Another point to note is that from the point of view of the stationary observer, the initial velocity of the orange is the summation of the horizontal velocity of the travelator and the vertical velocity at which the ball left my hand. The orange “inherits” the velocity of the travellator, so to speak. If I had merely released the orange, it would have been a horizontal projectile motion to the stationary observer.