The attitudes that are regarded as those of typical adults are those that come in direct conflict with those of the children.

Despite of being rich and privileged, the Burnell sisters bypass social ranking and go against their mother's ruling that they are not to speak to the Kelvey sisters. In contrast, their mother tries to instill in the girls the concept of social consciousness and differentiation by class. This merely because the Kelvey's reputation is preceded by that of their mother, whose behavior is questionable. 

Similarly, Aunt Beryl is very aware of social differences and even throws out the Kelvey sisters after they accept Kezia Burnell's invitation to see the doll's house.

How dare you ask the little Kelveys into the courtyard?" .."You know as well as I do, you're not allowed to talk to them. Run away, children, run away at once. And don't come back again," said Aunt Beryl. And she stepped into the yard and shooed them out as if they were chickens.

Notice how the adults are the ones who initiate and instigate the need for separation. As a result, some of the girls imitate the adults on the playground and they equally distance themselves from the Kelvey girls and joke about them.

Hence, the behaviors that typically manifest in adults are class consciousness, social differentiation, and the need for a social hierarchy where the rich come out on top.