Positively they need acclimation.
Float the bag in the tank for 15--20 minutes so that the temp can equalize.
Open the bag and pour a shot glass of water from the tank into the bag.
Let the open end of the bag hang over the side of the tank. Do whatever it takes to keep the bag in the tank, but don't let the open end of the bag spill into the tank.
Every 10 or 15 minutes, take another shot glass and pour water from the tank into the bag.
If the bag gets full, take it to the sink and dump out 50% of the water. It helps to squeeze the bag down low so the critters can't flow out past your hand where it is being squeezed.
Put the bag back in the tank and pour another shot glass of water into the bag.
After you've trippled the volume of the water in the bag--couple hrs of pouring shot glasses in every 15 minutes--your done.
NEVER NEVER NEVER NEVER put water from that bag into your tank. You don't know where it's been. I NEVER introduce water from another source, into my tank. NEVER
Don't touch zoanthids with your bare hands. They hold one of the most toxic organic chemicals known on the planet. If one of them squirts and it gets in your eye or in an open cut--your taking a miserable trip to the hospital--RIGHT NOW!! Use hemostats to handle them or wear rubber gloves. Wear safety glasses. Keep your head back. Don't point them at yourself, they tend to shoot straight out.
Mushrooms are just about harmelss--I think. But it wouldn't hurt to treat them with the same care as a zoa. They need to be acclimated in the same manner, but I don't think they are dangerous.