A Cyclone Phrase™ is one in which
for each word, the letters in the first half of the word (including the middle letter, if there is one) are in alphabetical order, and the letters in the second half of the word (again including the middle) are in reverse alphabetical order.
The one exception is "an old bum begged". The word 'old' does not have this property: the first half, 'ol', is not in alphabetical order.