In what sort of circumstances did you hear the phrase? For example, it occurs to me that the football season starts in August and the first few weeks of games are, more or less, 'autumnal'. Perhaps it was a reference to how managers initially run things, try out new players, make decisions on playing tactics and so on. Could that 'breaking-in' period be what it's all about?
I honestly can't remember, QM. I know it popped up as titles of pop/dance (?) singles a few years back and actually heard it dropped into a conversation and thought it an unusual phrase then. I've been engine-searching the phrase, but am really none the wiser.