I know that AA domestic flights have only 2 cabins -> economy and domestic first

Do you ever see a case on when you book a long-haul in J within an alliance, the correspondance flights within the USA are in Y ?
Because, I thought that the corresponding cabin class is always the domestic first, but maybe i'm wrong.

Also, the strange thing here it that my first flight between ORD and SJC is confirm in domestic First, and I was able to book my seat.