Yeah, I did get all that, actually
. We've made me curious, so found out:
This effect is called "seasonal lag", like what I meant when I guessed the September warmth is an "afterglow" and the January cold an "after-effect". The absorption and release of the sun's energy on land & oceans takes quite a while longer than the solstices, due to its (thermal) "inertia", they keep the warmth and cold longer, don't react that quickly to the length of sunlight, water even more than earth. I guess like warm ocean water on a cold summer's day.
So real "summer" & "winter" do actually
not start with the solstice, it'd be more precise to call that the 45 days before & after the "hottest / coldest days" summer / winter, scientist say.