I am far from an expert but:
My mother-in-law always told me that one could prune their chrysanthemums UNTIL the first of July
(I took it to mean the first part
that will still give them time to form buds and bloom. I do not think one has to prune them though---I always did mine, so they would not get so tall that they would droop over.
Someone with more experience should come along & help you.