I think you may have a step missing here. The cog icon in the VST panel doesn’t assign instruments to a plugin, it sets up the expression map (which tells Dorico how to convert Playing Techniques into keyswitches, etc). The assignment of an instrument to a plugin is done in the ‘Track Header’ in the left side of Play Mode (where you have ‘Trombone’ followed by ‘—’).
However, if you are using the default HALion sounds then you shouldn’t ever need to do this by hand. I have just tried this now and I can’t reproduce the problem. I created a new score and then added an oboe player using the ‘Add Solo Player’ button in Setup Mode. The new instrument show up in the mixer as ‘HSSE Oboe’.
Can you describe the steps that get you into this state?
You should find that Play → Load Unassigned Instruments will ensure that these other tracks get assigned, or you can do Play → Apply Default Playback Template to do a reassignment for all instruments.