I had pretty much the exact same thing happen to me.... I'll be interested to see what people have to say. I'm nervous mine won't come up now!

having the same problem, I'm in zone 10. It has been raining almost every single day. some of my Dahlias are sending up new shoots and some have I haven't noticed any growth at all. only one have dried out, and I can't understand why...also interested in what more experienced growers have to say, since this is my very first time and my zone isn't really recommended

" will this rain cause them to rot?"

Soggy soil that takes longer then a day to drain often causes dahlia tubers to rot. Dig down to the same level as your tubers (a foot away so you don't hurt their feeder roots), and see if water gathers in your hole. If so, you have a drainage problem.

The tubers have 'breathing holes' called lenticels along the sides, and when too wet for a prolonged period of time, often expand to spongy slits that can look quite alarming. Other then making it difficult to write on the tuber after dividing in the fall, the bumps are harmless. But they DO act as a warning sign, when caught early enough, that the soil is too wet for too long.

(technically, the lenticels "functions as a pore, providing a pathway for the direct exchange of
gases between the internal tissues and atmosphere" through the outer skin of the tuber)

Digging trenches around your beds can give the water somewhere to go, other then around the tubers. Raised beds are good, as well. In low areas of my garden, I do both, digging trenches and mounding the excess soil up 6 inches so the tubers can be planted at ground-level. Often I see water sitting in the trenches, and I haven't lost tubers to rotting since I've implemented that double technique. What would be better yet is if I had a place to drain that water farther away from the beds.