Homer Morisson

Definitely works like that with the multiple ranks, on that I am sure as this is exactly what I could observe throughout a multitude of naval battles... I'm 30 hours in and story-wise have just visited the Queen for the first time in Neketaka, i.e. haven't even been to her first mission yet... have rather spent my time becoming rich(-ish) and getting a more powerful ship first, and by now I have a couple of Master level crew, they definitely had a multitude of "gained a rank"-ups, compared to only three level ups to go from 1 to 4.
 
You as the captain btw can level up until level 5, that much at least is explained in the Tutorial section of the whole Journal menu.

Check your formation setting and distance to your main character during dialogues -- I have found that there is a very, very small area around the main char only where those party assists are being registered/counted... for example when using a custom formation and having the main char 2 or 3 squares away from the rest of your party, during dialogues you would likely not get any assists.
 
If you manually make sure that all your party members are directly next to the NPC and main char before starting the dialogue, you will however see those assists suddenly working.
 
@Caleb:
 
I would suggest making that area at least 25% bigger, because it really does lead to me having to manually reposition my guys from their regular formation for every single dialogue, just to make sure that the game actually knows that I want them to be involved in this discussion.