Checked the parasite interaction and it seems to be correct to me. So in that scenario lets say you have bard and mate. Both are level one but the mate will be effectively level 2 due to bard boost. Then you get parasite trinket and nothing happens to either of those crew members. You get a third one, lets say navi and they'll be auto upgraded to level 2 and with the bard boost be effectively level 3. So the effect only applies to new crew members you receive, not retroactively to existing ones.