What makes you so sure Oda is going to use the same kind of depiction to hype characters every time Kaido is hurt or cut by someone? Simply cutting Kaido is no longer a feat worthy of highlighting when lesser characters accomplished it multiple times already.
Zoro and Killer are just getting started. They did damage Kaido and impressed him but they didn't do anything of significance for it to be elevated at Red Rock level. Their attacks will be highlighted when they do something that can surprise Kaido.
Drawing blood from Kaido matters. First time he got Oden flashbacks. Second time he started seeing Legends of the past in the one who did it.
Going from that, to it being a hidden achievement in a combo attack with Killer that happens in the wake of the Captains launching individual attack makes absolutely zero sense.
Zoro drawing blood will be the most significant first step towards being able to open Kaido's scar. It will be it's own moment. It's not going to be something you have to assume it happened, and assume it caused an unseen injury.
How is this not intuitive and requires further discussion ? Nothing about that scene and it's context in the chapter makes sense to lead to this interpretation.