I think that's the normal Smith Family and Summer C-131 simply decided that she was gonna use the new pronunciation of Parmesan from now and on.

@Bonus Person but in nomortland Jerry explicitly says they say parmesan weirdly

That doesn't contradict my reply, I was saying Summer adopted that weird pronunciation.

Think of it this way: An american who moves to England might start pronouncing words the british way after living there for a while.

The same thing happens here. Summer pronounces "Parmesan" weirdly in That's Amorte because she got used to it after staying in the Parmesan Dimension for a while.