I dig the clump out first. Wash off as much dirt as I can with the hose. At times that is enough to tease the fans apart and I don't use the daylily divider.
When the clumps are too big and tightly grown together, after washing with the hose, I put the whole clump into a tub of water and let it sit for at least several hours, sometimes even overnight. After that I tease as many fans out as possible from the outer edges. But usually the center (or majority of the clump is too tight) THAT'S when I have to use the DD. These are usually clumps that should have been divided several years ago. I break the clump into several smaller clumps (using the DD) and swoosh it around in the tub of water until I can get the roots untangled.
Of course using the DD will cause a bunch of broken roots and even fans. But when the only other alternative is to cut the clump with a knife or shovel...that's when this tool is great. At least for me. If I recall I paid about 60 something for it. I don't regret the purchase.
Any over grown (neglected) clump is difficult. I'll put a lot of work into a clump but if I'm already breaking fans off, then it's time for the DD. IMHO