Perfectly normal for the individual flowers to last only a day, two at most. The hotter the weather, the faster they fall -- I've seen them drop in about 6 hours during 96 degree heat.

Well, you can't really "fill the hole" because the dormancy only lasts a few weeks -- soon new leaves will emerge that will grow into a basal clump of foliage and persist until the hard frost. The plant needs to be able to grow these leaves to build up for next year, and if you plant something else over the top of it that could out-compete it.

Double Gem Tangerine appears to be Papaver rupifragum (Spanish poppy) which may not go dormant --several listings say it doesn't even in high heat/humidity, though it might if we get triple-digit hear for an extended period.

I would wait and see if it does in fact go dormant. If it does, a nice tropical plant like a sun coleus should fill the gap until fall when the poppy comes back.

I wintersowed "Mrs. Bradshaw" geum which bloomed this Spring and were beautiful. It seemd mine lasted a few weeks, because it was planted beside of "Brilliant" oriental poppy which was almost the same color and what a beautiful sight. I will have to pay more attention to how long a new plant blooms, etc.
I would say it's stems appeared to grow outward, like whimsical and I don't know if that is right word to use. When they finished blooming, I cut it back to its basal plant but it is putting out new leaves in that area. Since it was my first experience with this plant, I really did not know what to expect. Everything in gardening is trial and error and that was one of my experiments I guess. Can you tell I'm an impatient gardener? Come the Fall, I may dig that plant up and move it to a different location.