Various enzymes are active between a quite a large temperature range including both amylases but they have optimal temperature ranges at which they are favoured. They also have optimal pH and other conditions but temperature when hydrated is the most important as far as I understand. Alpha will work at 60 and beta at 70 but beta will be favoured at 60 and alpha at 70 (if that makes sense).
Given that alpha makes longer chains and beta shorter, beta can continue to chop up the chains that alpha has already had a crack at. Give it time and it can reduce that stuff down.
As far as I understand amylase conversion can happen in 20 degrees (for example) if the malt is hydrated - it's just a very slow process and that temp may favour other enzymes (and likely microflora) so their effects will make themselves known much more quickly.
@bradsbrew - true.