Month of tropical storms, just not October (5)

I believe the answer is:

april

I'm a little stuck... Click here to teach me more about this clue!

'month' is the definition.
(I know that Gregorian calendar month is a type of month)

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for april that I've seen before include "4th month" , "'All in an ... evening' (Katharine Tynan)" , "Fourth month" , "Thirty days in spring" , "TS Eliot's 'cruelest month'" .)

I've seen this clue in the Sydney Morning Herald.

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