I hope my Gigantea will not spawn, at least if she is a female, but keep them and take in the sperm and release fully formed babies.
It is my understanding that giganteae are internal brooders and that they behave exactly as you describe. This is based on second-hand, but pretty reputable observation from someone who was indirectly successful raising them in Palau. (I say indirectly, because it was not the primary purpose of the facility, so very little effort was put into formalizing and improving the aquaculture process - it "just happened"). Based on this person's experience, S. gigantea males trigger the spawning behavior when they release their sperm into the water. The females ingest the sperm where it internally fertilizes the eggs. At some point in the future (unknown), the females release tiny juveniles which then broadcast colonize the area. They are apparently very small at this stage and look like hydras and not at all like adult giganteae. It should be noted that other species of anemones are also internal brooders, so this behavior is not unique to S. gigantea.
I have very little additional information on S. gigantea reproduction. The best I can do is to try to draw parallels from other anemone species. Dr. Anna Scott has been doing the most current work in this area, but she is only working with H. crispa and E. quadricolor due to her location. I have asked her about S. gigantea reproductive behavior and she cannot provide any additional information at this point since she has no first-hand experience with the species.
Based on some of her recent work, it may be that the internal brooding period within S. gigantea is 14 days or less (since this is roughly the point at which there are almost no free-swimming larvae left with related broadcast spawning anemones). With H. crispa and E. quadricolor, larvae can settle out and start to develop arms as soon as 10 days after spawning, if conditions are optimal. E. quadricolor is a little faster because the eggs are larger and the larvae are also larger. The eggs of E. quad and H. crispa both contain zooxanthellae, and the larvae and juveniles develop with zooxanthellae already present in their tissues. It appears to be the only source of nutrients for at least the first three weeks of life, since it takes around three weeks for juveniles to develop a mouth. There is a lot less known than unknown at this point.
One thing I can say pretty certainly - rearing gigantea babies from the juvenile stage forward will require a specialized setup. The environment of a typical reef tank probably does not provide for the needs of the juveniles, and they would also be easy prey for any critter in the tank that wanted a quick snack.