This is normal. I began with one tuber four years ago and now have 32 plants in the ground. I never dig them up. The largest plant is now over 6 feet tall with several others nearing that size. Many others are only 1 foot tall.

In Japan where these plants are grown as a food crop the tubers are dug up and split into quarters through the apical meristem and replanted immediately to quadruple the number of plants that can be harvested.

In your zone which is similar to mine the plants can stay in the ground year round but if you wish to store them just wrap them in damp burlap and place them in a dark place until the plant begins to emerge from dormancy. Once a plant begins to emerge then plant it.

I store mine dry, in a paper bag or on a shelf.

geoforce:
I thought I'd share a photo of my new A. konjac that I purchased about a month ago on ebay. The pot it's growing in is an 8 inch pot. To my surprise it already has a second one that popped up beside it. This is my first year growing these and I'm hoping to keep it in this pot once it dies back in the fall. If I thought I could keep it growing inside all winter I'd try that, but I'm not sure if it would survive or it needs to go dormant.
{{gwi:389366}}From Garden 2009

A. konjac is very hit and miss in the ground here.....some survive, many die in our wet/cold winters so I dig many every fall to keep them going......leave them dry as a bone on a shelf.

dpolson, they will go dormant when they are ready......you can not keep them evergreen even if you wanted to....let the plant be your guide :o) Dan