I've never seen Disney ever use the exact astrological definition of the seasons when they throw around seasonal dates.
It's also rare for people in general to go by strict dates. E.g., in NJ, grade school goes past the start of astrological Summer until the end of June, and they go back to classes the first week of September before astrological Summer ends.
But when we say "the kids have off of school for the Summer," no one in their right mind would say, "Hey, how come they're in session in late July and early September!!? It's Summer!!!!"