Answer: In general, viburnums would not be pruned much if at all, but you could remove a stray growing branch or two at any time in spring or summer without causing a discernable difference in the blooms. You could also thin the plant by removing branches by cutting deep within the shrub. Late spring would be a good time to do that.
Rust is usually worse in wet weather with cool nights so it may disappear when the weather warms up -- if it also dries out a bit. However, control is similar to that used for black spot: increase air circulation by proper pruning, avoid wetting the leaves, especially in the evening, remove and destroy infected leaves, be fastidious about fall clean up and strip off all leaves then top up the mulch with a fresh layer. You can also use neem during the growing season.
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