I'm pretty sure regular Kayn's passive meter doesn't work as intended
I have ~30 games on Kayn, and it really feels like that the champions you fight early on don't contribute to whether you become Shadow Assassin or Darkin. I'm not talking about how little they contribute to the meter in the early game; I think the amount is supposed to scale, and that's fine. I'm talking about the choice you get between the two. You can fight ranged champions for the first 99% of your meter, but if you top off your meter from a melee champion, you'll be able to choose Darkin. Same thing works in reverse - you can fight melee champions for the first 99% of your meter, but if you top it off from a ranged champion, you'll get Shadow Assassin. The tooltip/wiki says that you'll be able to choose based on which one you damage more, but I think it really just depends on which one you damage to fill it up.