The plants will die back in spring or early summer and produce tubers to withstand the dry conditions they experience usually during summer. Some species can actually be forced to keep growing during summer by keeping the light period short (e.g. about 10 hours). I tried this for D. auriculata and D. peltata plants which worked well for at least one season. However, I do not recommend this for regular culture.

At some stage in spring the leaves will start to blacken, usually starting at the outer parts first. Depending on the conditions and the species the plant may need hours to weeks for dying back. Especially on hot days some plants may die back quickly.
Once a plant has died back above the surface the subtrate should be kept moist for at least 4 more weeks as the tubers will need some time to form. As always, there are many differences between species as some have nearly completed tuber production whereas others like D. platypoda often only have stolons produced at that time. If you are not sure what to do, wait at least a couple of weeks and then carefully check the substrate for the status of tuber formation. Please keep in mind that each time you check you risk to damage tubers or stolons.

Each summer I find few plants which produce new growth instead of (or in addition to) tubers. Now it is up to the grower to decide what to do. After some trial and error I came to the conclusion that the best way of handling this situation is to carefully dissect the pot and separate resting tubers from plants producing new shoots. Forcing plants into dormancy does not work. Instead, the plants are most likely to die. And keeping the resting tubers wet during summer may result in a complete loss due to rot. Therefore, a separation seems to be the best option and so far worked well for me. The newly emerging plants may grow throughout summer and the full next growing season. I had this happening for many species. D. pallida, D. modesta, D. tubaestylis are just some of them.