That's the point.
You do have to be somewhat vague when talking about seasons. It's simpler to apply a general timeline to season, rather than month, which takes into count our different weather regions.
I could say late august-september is late summer to me but it could be fall or mid...
There's a hard molt where they look raggedy, naked and horrible and a soft molt where there will be feathers everywhere but no discernable cause. I have two hard molting and 4 that are soft molting.
As long as you don't see any active plucking and are sure their aren't pests, I wouldn't worry.
I've never seen birds molt in the fall, it's always been late summer or late winter.
There are several molts during a bird's first year, the biggest one is about when they hit a year, give or take a few months.
Several of my year olds months are molting right now and they look like heck...