Yes, the worst thing about tilling is breaking up rhizomes and stolons of grasses and thistle that will produce brand new plants. I suspect that all around the edges of the daylily bed, grass has invaded. Mulching will not cure this, as the already established grass will come up through the mulch. Barring a chemical approach, I suggest that you will need to dig and remove the grass at the edges, and probably need to dig some of the edge daylilies to extricate the grass roots from the plants. Then mulch.
