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 of July)

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.