I currently don’t have a machine with Dorico on it at hand, so I can’t prove it, but I do guess that the internal routing of HALion is messed up. Therefore, please open the HALion editor window and check where each slot is routed to. I guess that the violin and cello get sent to the same output port.
Yes, that’s usually the best approach. Use the Playback Template to set up the default playback and then change the sounds if required. If you load HSSE manually in the rack (as you would do in a DAW) then the MIDI channels won’t be set to separate outputs.