pathfinder 2e – Do innate spells use my main spell DC?

Clark is a gnome Cleric, and took First World Magic to gain a Electric Arc as an innate spell.

On level 7, he is Expert in divine spell DCs. Innate spells seemingly do not care about your tradition:

You’re always trained in spell attack rolls and spell DCs for your innate spells, even if you aren’t otherwise trained in spell attack rolls or spell DCs. If your proficiency in spell attack rolls or spell DCs is expert or better, apply that proficiency to your innate spells, too. You use your Charisma modifier as your spellcasting ability modifier for innate spells unless otherwise specified.

Does the lack of “appropriate tradition” in the highlighted section mean that innate spells always use your best DC?