My guess would be to keep an eye on it and get it out of there when it dies, especially if you have anything else in the tank that you don't want to die along with it. Never introduce an anemone into a tank that is not very stable. Your tank should never show any ammonia unless something large died and got left in there. Sounds like your 12g never had a chance to end up completely cycled, or you added a large number of inhabitants and caused a spike,
On the off-chance it does survive, you can try to get the salt level up about .001 per day until you reach 1.025. Are you using a properly calibrated refractometer to measure salinity? When it get's there you have to be diligent with keeping evaporation topped off.
With a small tank things happen very fast. Your salinity can be thrown off a fair amount just from evap. You need weekly water changes, stable temps, etc... Overall a stable tank with great parameters. Of course I'm sure you know the tank is too small, which is why you have the 55g cycling. However your small tank isn't stable either.
Don't take offense to this, but you really need to do a lot more research and get some more experience at keeping stable tanks before you go buying finicky animals that require perfect/near perfect/stable conditions.
Work on getting the salinity up, do your weekly 20% water changes, keep everything stable, and leave it alone. When you do your water changes make sure you let the water sit overnight after mixing, make sure the pH matches the tank, and make sure temp is the same. Try to avoid shocking the anemone with anything anymore.
I highly doubt it will survive, but try what was suggested and see what happens. If it starts to improve in a week or 2 try feeding it some frozen mysis or a silverside.
Good luck.