What kind of mulch?
Whatever it is, don't till it in.
Foliar fungal pathogen spores can not become vegetative and reproduce on dead organic matter, they need live tissue to become active. So your mulch and soil can harbor spores, but that's it. If those spores can get splashed up on the leaves then they can infect the leaves and reproduce.
Verticillium Wilt is caused by a soil born pathogen that infects through the roots. Mulch won't affect it one way or another.
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