From what I find online Dragon Arum is another name, or another type, of what I call Voodoo lily. Yes, it's normal for the plant to die back after blooming. Many little bulblets will form off the big bulb that has bloomed and will be coming up shortly.

My Voodoo lily blooms in April and the foliage comes up the end of May or early June so perhaps yours is on a different schedule. Perhaps we could trade bulbs sometime.

These are the April blooms on mine. Does yours look like this? It's the first time I've had three bloom at once ...

One of the blooms produced seeds which I'll plant and see if we come up with some baby Voodoo lilies.

I had very small bulbs and I think they needed to be planted in more sun (they were under trees). I had 1 bloom before it went dormant and provided seeds which I have planted. We'll see what happens. I usually have better luck with cuttings (which you could tell by the excessive number of plants in pots around my yard). Thanks for easing my mind.