Corals are some of the longest living animals on earth and I presume coral colonies like zoas technically can live forever….
So I would give them a few days to settle in
I think moving corals always stresses them out way more than we might think. Especially something that was just fragged. They’re coming from different parameters, different salinity, kh, ph, no3, mg, ca, etc. not to mention the rapid temp swings. It’s really amazing how a coral can withstand all of that over the course of a ~day or two. I wouldn’t worry. I had GSP and zoas that wouldnt open for days then some that would open right up.
Don’t do anything special. Do not dose anything especially if your tank is a one gallon pico reef. Just use some “reef” salt like reef crystals or coral pro which contains proper levels of elements and that’s where all your elements come from. If your other corals are happy then your new ones will be too in due time.
Also, a golden rule is to always acclimate fish and corals however, I personally have never acclimated a coral. Granted I only have zoanthids, palys, gsp, and a frogspawn so that may not be the case with less hardy specimens. But I really feel like it’s best to just get them in the tank as quick as possible when lights are out and don’t mess with them for a day or two.
Dipping your corals— yes, I would do that for sure. I’ve had my luck so far with only buying from a single person who already dips them for me.