Produce a hostile reaction from Mills if not Prokofiev (7)

I believe the answer is:

provoke

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'produce' is the definition.
(thesaurus)

I cannot understand how the rest of the clue works.

(Other definitions for provoke that I've seen before include "Incense" , "Make angry or incite to action" , "Goad" , "Stimulate (a reaction)" , "Irritate - arouse" .)

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

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