Weird, right? Your flying cups curved upward. This uplifting bit of lift occurred because you put a spin on the cups as they were launched.
During launch, the rubber band not only propels the cups forward, but also gives them a rapid backspin. As the backward-spinning cups fly through the air, a thin layer of air—called the boundary layer—gets dragged along for the ride and flung downward by the backspin. In accordance with Newton’s Third Law of Motion, every action has an equal and opposite reaction: The downward force on the air results in an upward force on the cups.
This trick, known as the Magnus effect*, is well known to baseball pitchers. By varying the direction and rate of spin of a pitched ball, a pitcher can create a variety of wildly veering pitches: curveballs, fastballs, screwballs, and sliders. The stitches on a baseball add to the trickery; not just decorative, they assist in deflecting air sideways, increasing the deflecting effect of the spin.
Soccer players, too, make use of the Magnus effect to launch balls that seem to have a mind of their own, diving down or swerving sideways into the net.
* Note: Technically, on a cylinder, the Magnus effect is more properly called Kutta-Joukowski lift. But go ahead and call it the Magnus effect.