after asking her where shes going shes says "no dad, the washitsu!" in the next panel she says "i want to introduce my friends properly. we need the formal sitting room." no notes or anything
in the official translation it first uses omase-san and late explains it means adult-like, so your translation was fine. precocious is a better translation but i feel he wouldnt use an uncommon english word to describe what omase means.