Origin can be trigged:
- by MIDI coming on the "Program mode channel" if a single program is loaded
- by MIDI coming on the MIDI channels of the zones (which can be seen either in the Multi/Slots or in the Multi/Zones page) if you are in Multi mode
- and in all cases it can receive program change messages on the "Master control channel"
So if it behaves like if all MIDI channels in Cubase were triggering Origin, it probably means that in fact Cubase is sending always on the same channel. You should verify the configuration of your Cubase project.
Anyway, a "Local on/off" parameter would't have helped you on that, because the purpose of the "local off" mode is to make the synth respond only to external MIDI, while in "local on" mode the synth respond to the external MIDI AND to the integrated keyboard. Since the Desktop version has no integrated keyboard the local on/off parameter is not useful.