Answer: You can mulch your perennials before, during, or after they come up. They will grow through the mulch. I usually wait until the plants a peeking through, then mulch around them.
In the fall, just leave it there to decompose as you suggest. You can add more to help protect them from winter frost, heaving, etc.
You're definitely on track to having a good garden. Keep up the good work!
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