The same CV produces opposite results when patched to the V/oct input and the individual Rise and Fall CV inputs. Why?

Even though both inputs can perform the same task, i.e., modifying the length of the rising and falling segments of the generated function, their concept is the opposite.

Rise and Fall CV inputs are designed to control the duration of the individual segments so that higher voltages provide more extended envelopes or LFOs. In contrast, the V/oct input is used mainly to control the pitch of a generator that is oscillating at audio rate: in this latter scenario, higher voltages equal to higher notes, i.e., shorter cycles.