It is not safe to assume at all. All carpets be it short or long tentacle carpets are mostly sequence spawners like many corals, where they all spawn at the same time. Furthermore, when carpet anemones split they are not usually the the same size. So, it is a safe assumption that in such an event those eggs will be fertilized and settle out near the parents and would be of similar size. A number of reefers and public aquariums have had carpet spawns and in most case it is sexual. Very few anemones are asexuality slippers/binary fissioners but are much more Basal Laceration. Most anemones are Dioecious but a some are Hermaphroditic or Parthenogenic. In my book on the biology of anemones out of ~ 15 species of anemones only one of them is know for fission. There is also very little documented evidence in the wild for carpets on spitting, most are seen in sexual spawning. I'm not saying they never split but it is rare. Even BTA are rare in the wild for splitting. But yes anemones can repro of various means. Very little is know about the % of repro by carpets from x, y or z type of repro. The rule is "Typically, anemone larvae have a planktonic developmental phase before settling."but a good exception to that is the famous cloning green,
Anthopleura sola known for its clone wars
. All anemones are capable of spitting but it does not me it is the preferred means of repro.
But here is a H. magnifica splitting in an aquarium.
However, with all that said above,
H.magnifica carpets spawn more than once a year. One study showed that
H. magnifica went through asexual rerpo in the winter. This study also seems to show the spitting is highly induced by the presence of clown fish and the growth rates of the hosted anemones where much more than the unhosted anemones by 3x. So, it seems that in short, splitting is more induced by stress, host fish and is in the winter spawn. So, I will take back it is rare but mostly induce by host fish for what ever reason
This is a recent study I have not seen till now in Coral Reefs.
Holbrook, SJ; Schmitt, RJ (2005). Growth, reproduction, and survival of a tropical sea anemone (Actinaria): benefits of hosting anemonefish. Coral reefs [Coral Reefs]. Vol. 24, no. 1, pp. 67-73