I say FWIW, look at the old Sumo traditions for the model of Sempai, Kohai thing and what it is all about.
But ummm...it seems different people put different twists on it. I have say, I was told the same thing as Josh wrote. I think this is a complicated situation, but what I was told and practiced is each class is different and thus follows what Josh said about who starts first. In one class your Kohai, but in the other your Sempai, and it stays that way.
It is I think the S/K relationship and model is a very difficult thingy in martial arts. The is similarities to a page and a knight (if that helps) and yet it is something different in societies outside Japan. Because the way the Japanese do it, they have their own rules and protocol and stuff which isn't widely known. There is, I am told, variations even in that depending on the art. S/K relationship is complicated practiced as intended.
I am saying I'd go with Josh on this one if that helps.