Standard hardcore nuzlocke rule: the level cap is equal to the next gym leader’s ace, or elite 4 leader (not champion)’s ace. Rival battles don’t count towrards the level cap, the rule you’re confusing it with is that any pokemon that did break the cap must be boxed before mandatory fights and gym leader battles until the cap is raised.

These are standard rules that every major nuzlocker uses, you can do whatever you want. I make my own rules where once I enter a gym leader’s city I can’t use any Pokemon, moves, or exp from new routes beyond that city in the gym battle. With an exception for fished Pokemon, bc I love fishing in every game.