En otoño las hojas se ponen rojas y doradas.


In the fall, the leaves turn red and gold.

Since this an irrevocable process, I think “se vuelven” would work as well, right?

Both “ponerse” and “volverse” can be used to describe a change, but “ponerse” often implies a more temporary or superficial change, while “volverse” can suggest a more profound or lasting change. So, I would say that you are correct indeed.