I was given a few of these plants three or maybe four years ago, the small one was small, and the bulb was cut in half almost when I planted it. The larger one was a nice large plant and had a full healthy bulb, it has grown and multiplied quite nicely. I was told it was a Peruvian Daffodil by the person who gave it to me, and that is what I always think of it as being. Mine blooms in July, so it will be a while before I see blooms this year. I don't do anything really special for it, it is planted in the ground and receives no special care. I water it occasionally when things get really dry along with the other plants.
My large clump:
My small plant:
Showing some amaryllis next to it for comparison:
Showing the base and the increases:
The blooms from last July:
I just realized both the one you have and the one you ordered are both called Peruvian Daffodil, so now I have to determine which one I actually have.
Well, they all look and sound alike to me, so I'll just call mine Peruvian Daffodil.
Finally found a site that says Hymenocallis harrisiana, is a deciduous species, and mine stays green all year and never sheds it leaves. So best I can tell mine is actually Peruvian Daffodil (Ismene x deflexa).