My question is, what determines a sempai versus kohai. Is it time? If so then that means everyone before you will always be your sempai, even if you go up and pass them in rank. Is it rank? If so, then if someone passes you in rank, they become your sempai and you revert back to kohai. Is it ability? If so, then those lower then you who happen to be more gifted in something would be your sempai in some circumstances. Does previous experience come into play at all (whether it is aikido or another style)? Does age get put in the equation? If so, then my husband would always be sempai because he is significantly older then I am.
Can someone be your sempai in one thing and your kohai in another? For instance, I take iaido and am more familiar with the sword. In aikido we also do a lot of work with the bokken. I sometimes work with a 5th kyu (I'm a 6th) kyu, who is my sempai. However, he isn't too familiar with the bokken because he doesn't attend the weapons class that often and he doesn't take iaido. Does that mean because I am more experienced with the bokken that I am sempai for that moment? Apparently, sensei does not treat them as separate classes and the sempai/ kohai relationship can spill over into the other class. Does that mean if someone who is my sempai in aikido comes into iaido that I must move down the line and treat them as my sempai in iaido as well?
Sempai-kohai is a relationship of seniority. As such, it never changes. Someone who starts the day before you is (technically) always your sempai, no matter how you change in rank and/or actual skill level. One can be a sempai in one thing (having started earlier than the other person) and kohai in another (having started later than the other person in that thing), but in the case of a single dojo teaching both aikido and iaido, sempai would be determined by who joined the dojo first.
All that said, it sounds like your sensei doesn't have a particularly nuanced understanding of the concept. In Japan, in an adult dojo, sempai-kohai relationships aren't particularly salient, compared to rank or actual ability.