Thank you for your question, Cathryn.   First, here is a link to an article with various problems dahlias suffer.   Dahlia tuber rot is caused by a specific fungus – Botrytis cinerea.  As you can read from these dahlia care instructions, removing your tubers, treating them with a fungicide, and storing them appropriately will go a long way toward preventing this problem, which flourishes in cool, wet soil.  Here is another WSU Extension article on the same topic.  Be sure to destroy the tubers that are no longer helpful.  (Don't compost!)

The other major thing you need to change is putting plastic over your garden. If it doesn't exist in the forest, it doesn't belong in your yard! When you put down plastic, you not only keep the soil from getting needed winter moisture, but you cut down/out the oxygen in the soil and make it a paradise for fungi that need cool, damp environments.    Of course, if your tubers are stored appropriately elsewhere, they won't mind.

Covering the soil with the leaves is fine. It not only protects the soil from compaction, as a mulch, but those same microbes (and many others) consume or break down the fiber and enrich the soil by replenishing nutrients. So, this is probably how the whole problem started. You probably don't need to dig all that soil out, because if it is turned (gently!) and exposed to the air, the pathogen will not be in the environment (cool, dark and wet) that they need.   I'd keep turning it for a few weeks before planting anything else. You can clean your garden tools with alcohol, but you should be doing that anyway to prevent the spread of other pathogens. Also true of any pruning tools.

I hope this is helpful for you.  Write back with any other questions.  Good luck!